Modelling Uncertainty of Stream Networks Derived from Elevation Data Using Two Free Softwares: R and SAGA

Affiliation(s)

Laboratoire 3E, Ecole Nationale des Ingénieurs de Sfax, Sfax, Tunisia.

Unité de Recherche Dynamique des Bassins Sédimentaires, Paléoenvironnements et Structures Géologiques, Département de Géologie, Faculté des Sciences de Tunis, Université Tunis El Manar, Tunis, Tunisie.

Compus de Beaulieu, Université de Rennes, Rennes, France.

Laboratoire 3E, Ecole Nationale des Ingénieurs de Sfax, Sfax, Tunisia.

Unité de Recherche Dynamique des Bassins Sédimentaires, Paléoenvironnements et Structures Géologiques, Département de Géologie, Faculté des Sciences de Tunis, Université Tunis El Manar, Tunis, Tunisie.

Compus de Beaulieu, Université de Rennes, Rennes, France.

ABSTRACT

Stream networks are considered important units in many environmental decision making processes. The extraction of streams using digital elevation models (DEMs) presents many advantages. However it is very sensitive to the uncertainty of the elevation datasets used. The main aim of this paper is to implement geostatistical simulations and assess the propagated uncertainty and map the error of location streams. First, point sampled elevations are used to fit a variogram model. Next two hundred DEM realizations are generated using conditional sequential Gaussian simulation; the stream network map is extracted for each of these realizations, and the collection of stream networks is analyzed to quantify the error propagation. At each grid cell, the probability of the occurrence of a stream and the propagated error are estimated. The more probable stream network are delineated and compared with the digital stream network derived from topographic map. The method is illustrated using a small dataset (8742 sampled elevations) for Anaguid Saharan platform. All computations are run in two free softwares: R and SAGA. R is used to fit variogram and to run sequential Gaussian simulation. SAGA is used to extract streams via RSAGA library.

Stream networks are considered important units in many environmental decision making processes. The extraction of streams using digital elevation models (DEMs) presents many advantages. However it is very sensitive to the uncertainty of the elevation datasets used. The main aim of this paper is to implement geostatistical simulations and assess the propagated uncertainty and map the error of location streams. First, point sampled elevations are used to fit a variogram model. Next two hundred DEM realizations are generated using conditional sequential Gaussian simulation; the stream network map is extracted for each of these realizations, and the collection of stream networks is analyzed to quantify the error propagation. At each grid cell, the probability of the occurrence of a stream and the propagated error are estimated. The more probable stream network are delineated and compared with the digital stream network derived from topographic map. The method is illustrated using a small dataset (8742 sampled elevations) for Anaguid Saharan platform. All computations are run in two free softwares: R and SAGA. R is used to fit variogram and to run sequential Gaussian simulation. SAGA is used to extract streams via RSAGA library.

Cite this paper

H. Achour, N. Rebai, J. Driessche and S. Bouaziz, "Modelling Uncertainty of Stream Networks Derived from Elevation Data Using Two Free Softwares: R and SAGA,"*Journal of Geographic Information System*, Vol. 4 No. 2, 2012, pp. 153-160. doi: 10.4236/jgis.2012.42020.

H. Achour, N. Rebai, J. Driessche and S. Bouaziz, "Modelling Uncertainty of Stream Networks Derived from Elevation Data Using Two Free Softwares: R and SAGA,"

References

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[10] C. Chen and T. Yue, “A Method of DEM Construction and Related Error Analysis,” Computers and Geosciences, Vol. 36, No. 6, 2010, pp. 717-725. doi:10.1016/.12.001

[11] Q. Zhou and X. Liu, “Error Analysis on Grid-Based Slope and Aspect Algorithms,” Photogrammetric Engineering and Remote Sensing, Vol. 70, No. 8, 2004, pp. 957-962. doi:10.1016/.07.005

[12] L. D. Raaflaub and M. J. Collins, “The Effect of Error in Gridded Digital Elevation Models on the Estimation of Topographic Parameters,” Environmental Modeling and Software, Vol. 21, No. 5, 2006, pp. 710-732. doi:10.1016/.02.003

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[14] S. P. Wechsler, “Perceptions of Digital Elevation Model Uncertainty by DEM Users,” Urban and Regional Information Systems Association Journal, Vol. 15, No. 2, 2003, pp. 57-64.

[15] M. J. Hannah, “Error Detection and Correction in Digital Terrain Models,” Photogrammetric Engineering and Remote Sensing, Vol. 47, No. 1, 1981, pp. 63-69.

[16] T. Q. Binh and N. T. Thuy, “Assessment of the Influence of Interpolation Techniques on the Accuracy of Digital Elevation Model,” Journal of Science, Earth Sciences, Vol. 24, No. 4, 2008, pp. 176-183.

[17] T. Q. Binh and N. T. Thuy, “Assessment of the Influence of Interpolation Techniques on the Accuracy of Digital Elevation Model,” Journal of Science, Earth Sciences, Vol. 24, No. 4, 2008, pp. 176-183.

[18] K. W. Holmes, O. A. Chadwick and P. C. Kyriakidis, “Error in a USGS 30-Meter Elevation Model and Its Impact on Terrain Modeling,” Journal of Hydrology, Vol. 233, No.1-4, 2000, pp. 154-173. doi:10.1016/S0022-1694(00)00229-8

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[20] Q. Zhou and X. Liu, “Analysis of Errors of Derived Slope and Aspect Related to DEM Data Properties,” Computers and Geosciences, Vol. 30, No. 4, 2004, pp. 369-378. doi:10.1016/.07.005

[21] M. F. Goodchild, “The Fractal Brownian Process as a Terrain Simulation Model,” Modelling and Simulation, Vol. 13, 1982, pp. 1133-1137.

[22] L. Polidori, “Validation de Modèles Numériques de Terrain, Application à la Cartographie des Risques Géologiques,” Unpublished Doctoral Thesis, Université Paris Diderot, Paris, 1991.

[23] D. Brown and T. Bara, “Recognition and Reduction of Systematic Error in Elevation and Derivative Surfaces from 7.5-Minute DEMs,” Photogrammetric Engineering and Remote Sensing, Vol. 60, No. 2, 1994, pp. 189-194.

[24] C. Lopez, “Improving the Elevation Accuracy of Digital Elevation Models: A Comparison of Some Error Detection Procedures,” Transactions in GIS, Vol. 4, No. 1, 2000, pp. 43-64. doi:10.1111/1467-9671.00037

[25] J. Oksanen, “Tracing the Gross Errors of DEM-Visualization Techniques for Preliminary Quality Analysis,” Proceedings of the 21st International Cartographic Conference, Durban, 10-16 August 2003, pp. 2410-2416.

[26] J. B. Lindsay and M. G. Evans, “The Influence of Elevation Error on the Morphometrics of Channel Networks Extracted from DEMs and the Implication for Hydro- logical Modelling,” Hydrological Processes, Vol. 22, No. 11, 2008, pp. 1588-1603. doi:10.1002/.6728

[27] X. Liu, “Airborne LiDAR for DEM Generation: Some Critical Issues,” Progress in Physical Geography, Vol. 32, No. 1, 2008, pp. 31-49. doi:10.1177/0309133308089496

[28] I. V. Florinsky, “Accuracy of Local Topographic Variables Derived from Digital Elevation Models,” International Journal of Geographical Information Science, Vol. 12, No. 1, 1998, pp. 47-62. doi:10.1080/136588198242003

[29] X. Liu and L. Bian, “Accuracy Assessment of DEM Slope Algorithms Related to Spatial Autocorrelation of DEM Errors”. In: Q. Zhou, B. Lees and G. A. Tang, Eds., Advances in Digital Terrain Analysis: Lecture Notes in Geo- information and Cartography, Springer, Berlin, 2008, pp 307-322.

[30] J. Schmidt, I. S. Evans and J. Brinkmann, “Comparison of Polynomial Models for Land Surface Curvature Calculation,” International Journal of Geographical Information Science, Vol. 17, No. 8, 2003, pp. 797-814. doi:10.1080/13658810310001596058

[31] G. Heuvelink, “Analysing Uncertainty Propagation in GIS: Why Is It Not That Simple,” In: G. Food and P. Atkinson, Eds., Uncertainty in Remote Sensing and GIS, Wiley, Chichester, 2002, pp. 155-165.

[32] T. Hengl, “A Practical Guide to Geostatistical Mapping,” University of Amsterdam, Amsterdam, 2009.

[33] D. Lanter and H. Veregin, “A Research Paradigm for Propagating Error in Layer-Based GIS,” Photogrammetric Engineering and Remote Sensing, Vol. 58, No. 6, 1992, pp. 825-833.

[34] S. Openshaw, M. Charlton and S. Carver, “Error Propagation: A Monte Carlo Simulation,” In: I. Masser and M. Blakemore, Eds., Handling Geography Information: Methodology and Potential Applications, Wiley, New York, 1991, pp. 102-114.

[35] G. B. M. Heuvelink, P. A. Burrough and H. Leenaers, “Propagation of Errors in Spatial Modelling with GIS,” International Journal of Geographical Information Systems, Vol. 3, No. 3, 1989, pp. 303-322. doi:10.1080/02693798908941518

[36] P. F. Fisher, “First Experiments in Viewshed Uncertainty: The Accuracy of the Viewshed Area,” Photogrammetric Engineering and Remote Sensing, Vol. 57, No. 10, 1991, pp. 1321-1327.

[37] J. Lee, P. K. Snyder and P. F. Fisher, “Modeling the Effect of Data Errors on Feature Extraction from Digital Elevation Models,” Photogrammetric Engineering and Remote Sensing, Vol. 58, No. 10, 1992, pp. 1461-1467.

[38] R. Liu and L. Herrington, “The Effects of Spatial Data Error on Forest Management Decisions,” Proceedings of the GIS Symposium, Vancouver, 1993, pp. 1-8.

[39] G. J. Hunter and M. F. Goodchild, “Modelling the Uncertainty of Slope and Aspect Estimates Derived from Spatial Databases,” Geographical Analysis, Vol. 29, No.1, 1997, pp. 35-49. doi:10.1111/j.1538-4632.1997.tb00944.x

[40] J. Oksanen and T. Sarjakoski, “Error Propagation of DEM-Based Surface Derivatives,” Computers and Geosciences, Vol. 31, No. 8, 2005, pp. 1015-1027. doi:10.1016/j.cageo.2005.02.014

[41] P. Goovaerts, “Geostatistics for Natural Resources Evaluation (Applied Geostatistics),” Oxford University Press, New York, 1997.

[42] A. Temme, G. Heuvelink, J. Schoorl and L. Claessens, “Geostatistical Simulation and Error Propagation in Geomorphometry,” In: T. Hengl and H. I. Reuter, Eds., Geomorphometry: Concepts, Software, Applications, Developments in Soil Science, Elsevier, Berlin, 2008, pp 121- 140.

[43] G. B. M. Heuvelink, “Error Propagation in Environmental Modelling with GIS,” Taylor & Francis, London, 1998.

[44] E. J. Pebesma, “Multivariable Geostatistics in S: The Gstat Package,” Computer and Geosciences, Vol. 30, No.7, 2004, pp. 683-691. doi:10.1016/j.cageo.2004.03.012

[45] O. Planchon and F. Darboux, “A Fast, Simple and Versatile Algorithm to Fill the Depressions of Digital Elevation Models,” Catena, Vol. 46, No. 2, 2001, pp. 159-176. doi:10.1016/S0341-8162(01)00164-3

[46] J. P. Ribeiro and P. J. Diggle, “Package ‘geoR’: Analysis of Geostatistical Data,” R Package Version 1.6-35, 2011.

[47] J. N. Lewin-Koh and R. Bivand, “Package ‘Maptools’: Tools for Reading and Handling Spatial Objects,” R Package Version 0.8-10, 2011.

[48] A. Brenning, “Package ‘RSAGA’: SAGA Geoprocessing and Terrain Analysis in R,” R Package Version 0.92-2, 2011.

[49] A. Brenning, “RPyGeo: ArcGIS Geoprocessing in R via Python,” R Package Version 0.9-0, 2011.

[50] T. Hengl, G. B. M. Heuvelink and E. E. Van Loon, “On the Uncertainty of Stream Network Derived from Elevation Data: The Error Propagation Approach,” Hydrology and Earth Sciences Discussions, Vol. 14, No. 7, 2010, pp. 767-799. doi:10.5194/hessd-7-767-2010

[1] T. X. Yue, Z. P. Du, D. J. Song and Y. Gong, “A New Method of Surface Modeling and Its Application to DEM Construction,” Geomorphology, Vol. 91, No. 1-2, 2007, pp. 161-172. doi:10.1016/.02.006

[2] J. Li and W. S Wong, “Effect of DEM Sources on Hydrologic Applications,” Computers, Environment and Ur- ban Systems, Vol. 34, No. 3, 2010, pp. 251-261. doi:10.1016/j.compenvurbsys.2009.11.002

[3] G. Peters and R. T. Van Balen, “Tectonic Geomorphology of the Northern Upper Rhine Graben, Germany,” Global and Planetary Change, Vol. 58, No. 1-4, 2007, pp. 310- 334. doi:10.1016/.11.041

[4] F. Troiani and M. Della Seta, “The Use of the Stream Length-Gradient Index in Morphotectonic Analysis of Small Catchments: A Case Study from Central Italy,” Geomorphology, Vol. 102, No. 1, 2008, pp. 159-168. doi:10.1016/.06.020

[5] C. J. Van Westen, E. Castellanos and S. L. Kuriakose, “Spatial Data for Landslide Susceptibility, Hazard, and Vulnerability Assessment: An Overview,” Engineering Geology, Vol. 102, No. 3-4, 2008, pp. 112-131. doi:10.1016/.03.010

[6] R. Nigel and S. D. D. V. Rughooputh, “Soil Erosion Risk Mapping with New Datasets: An Improved Identification and Prioritization of High Erosion Risk Areas,” Catena, Vol. 82, No. 3, 2010, pp. 191-205. doi:10.1016/j.catena.2010.06.005

[7] P. F. Fisher and N. J. Tate, “Causes and Consequences of Error in Digital Elevation Models,” Progress in Physical Geography, Vol. 30, No. 3, 2006, pp. 467-489. doi:10.1191/0309133306pp492ra

[8] S. P. Wechsler and C. N. Kroll, “Quantifying DEM Uncertainty and Its Effect on Topographic Parameters,” Pho- togrammetric Engineering and Remote Sensing, Vol. 72, No. 9, 2006, pp. 108-1090.

[9] V. Chaplot, F. Darboux, H. Bourennane, S. Leguedois, N. Silvera and K. Phachomphon, “Accuracy of Interpolation Techniques for the Derivation of Digital Elevation Models in Relation to Landform Types and Data Density,” Geomorphology, Vol. 77, No. 1-2, 2006, pp. 126-141. doi:10.1016/j.geomorph.2005.12.010

[10] C. Chen and T. Yue, “A Method of DEM Construction and Related Error Analysis,” Computers and Geosciences, Vol. 36, No. 6, 2010, pp. 717-725. doi:10.1016/.12.001

[11] Q. Zhou and X. Liu, “Error Analysis on Grid-Based Slope and Aspect Algorithms,” Photogrammetric Engineering and Remote Sensing, Vol. 70, No. 8, 2004, pp. 957-962. doi:10.1016/.07.005

[12] L. D. Raaflaub and M. J. Collins, “The Effect of Error in Gridded Digital Elevation Models on the Estimation of Topographic Parameters,” Environmental Modeling and Software, Vol. 21, No. 5, 2006, pp. 710-732. doi:10.1016/.02.003

[13] J. P. Wilson and J. C. Gallant, “Terrain Analysis: Principles and Applications,” Wiley, New York, 2000.

[14] S. P. Wechsler, “Perceptions of Digital Elevation Model Uncertainty by DEM Users,” Urban and Regional Information Systems Association Journal, Vol. 15, No. 2, 2003, pp. 57-64.

[15] M. J. Hannah, “Error Detection and Correction in Digital Terrain Models,” Photogrammetric Engineering and Remote Sensing, Vol. 47, No. 1, 1981, pp. 63-69.

[16] T. Q. Binh and N. T. Thuy, “Assessment of the Influence of Interpolation Techniques on the Accuracy of Digital Elevation Model,” Journal of Science, Earth Sciences, Vol. 24, No. 4, 2008, pp. 176-183.

[17] T. Q. Binh and N. T. Thuy, “Assessment of the Influence of Interpolation Techniques on the Accuracy of Digital Elevation Model,” Journal of Science, Earth Sciences, Vol. 24, No. 4, 2008, pp. 176-183.

[18] K. W. Holmes, O. A. Chadwick and P. C. Kyriakidis, “Error in a USGS 30-Meter Elevation Model and Its Impact on Terrain Modeling,” Journal of Hydrology, Vol. 233, No.1-4, 2000, pp. 154-173. doi:10.1016/S0022-1694(00)00229-8

[19] A. Felic?simo, “Parametric Statistical Method for Error Detection in Digital Elevation Models,” Journal of Photogrammetry and Remote Sensing, Vol. 49, No. 4, 1994, pp. 29-33. doi:10.1016/0924-2716(94)90044-2

[20] Q. Zhou and X. Liu, “Analysis of Errors of Derived Slope and Aspect Related to DEM Data Properties,” Computers and Geosciences, Vol. 30, No. 4, 2004, pp. 369-378. doi:10.1016/.07.005

[21] M. F. Goodchild, “The Fractal Brownian Process as a Terrain Simulation Model,” Modelling and Simulation, Vol. 13, 1982, pp. 1133-1137.

[22] L. Polidori, “Validation de Modèles Numériques de Terrain, Application à la Cartographie des Risques Géologiques,” Unpublished Doctoral Thesis, Université Paris Diderot, Paris, 1991.

[23] D. Brown and T. Bara, “Recognition and Reduction of Systematic Error in Elevation and Derivative Surfaces from 7.5-Minute DEMs,” Photogrammetric Engineering and Remote Sensing, Vol. 60, No. 2, 1994, pp. 189-194.

[24] C. Lopez, “Improving the Elevation Accuracy of Digital Elevation Models: A Comparison of Some Error Detection Procedures,” Transactions in GIS, Vol. 4, No. 1, 2000, pp. 43-64. doi:10.1111/1467-9671.00037

[25] J. Oksanen, “Tracing the Gross Errors of DEM-Visualization Techniques for Preliminary Quality Analysis,” Proceedings of the 21st International Cartographic Conference, Durban, 10-16 August 2003, pp. 2410-2416.

[26] J. B. Lindsay and M. G. Evans, “The Influence of Elevation Error on the Morphometrics of Channel Networks Extracted from DEMs and the Implication for Hydro- logical Modelling,” Hydrological Processes, Vol. 22, No. 11, 2008, pp. 1588-1603. doi:10.1002/.6728

[27] X. Liu, “Airborne LiDAR for DEM Generation: Some Critical Issues,” Progress in Physical Geography, Vol. 32, No. 1, 2008, pp. 31-49. doi:10.1177/0309133308089496

[28] I. V. Florinsky, “Accuracy of Local Topographic Variables Derived from Digital Elevation Models,” International Journal of Geographical Information Science, Vol. 12, No. 1, 1998, pp. 47-62. doi:10.1080/136588198242003

[29] X. Liu and L. Bian, “Accuracy Assessment of DEM Slope Algorithms Related to Spatial Autocorrelation of DEM Errors”. In: Q. Zhou, B. Lees and G. A. Tang, Eds., Advances in Digital Terrain Analysis: Lecture Notes in Geo- information and Cartography, Springer, Berlin, 2008, pp 307-322.

[30] J. Schmidt, I. S. Evans and J. Brinkmann, “Comparison of Polynomial Models for Land Surface Curvature Calculation,” International Journal of Geographical Information Science, Vol. 17, No. 8, 2003, pp. 797-814. doi:10.1080/13658810310001596058

[31] G. Heuvelink, “Analysing Uncertainty Propagation in GIS: Why Is It Not That Simple,” In: G. Food and P. Atkinson, Eds., Uncertainty in Remote Sensing and GIS, Wiley, Chichester, 2002, pp. 155-165.

[32] T. Hengl, “A Practical Guide to Geostatistical Mapping,” University of Amsterdam, Amsterdam, 2009.

[33] D. Lanter and H. Veregin, “A Research Paradigm for Propagating Error in Layer-Based GIS,” Photogrammetric Engineering and Remote Sensing, Vol. 58, No. 6, 1992, pp. 825-833.

[34] S. Openshaw, M. Charlton and S. Carver, “Error Propagation: A Monte Carlo Simulation,” In: I. Masser and M. Blakemore, Eds., Handling Geography Information: Methodology and Potential Applications, Wiley, New York, 1991, pp. 102-114.

[35] G. B. M. Heuvelink, P. A. Burrough and H. Leenaers, “Propagation of Errors in Spatial Modelling with GIS,” International Journal of Geographical Information Systems, Vol. 3, No. 3, 1989, pp. 303-322. doi:10.1080/02693798908941518

[36] P. F. Fisher, “First Experiments in Viewshed Uncertainty: The Accuracy of the Viewshed Area,” Photogrammetric Engineering and Remote Sensing, Vol. 57, No. 10, 1991, pp. 1321-1327.

[37] J. Lee, P. K. Snyder and P. F. Fisher, “Modeling the Effect of Data Errors on Feature Extraction from Digital Elevation Models,” Photogrammetric Engineering and Remote Sensing, Vol. 58, No. 10, 1992, pp. 1461-1467.

[38] R. Liu and L. Herrington, “The Effects of Spatial Data Error on Forest Management Decisions,” Proceedings of the GIS Symposium, Vancouver, 1993, pp. 1-8.

[39] G. J. Hunter and M. F. Goodchild, “Modelling the Uncertainty of Slope and Aspect Estimates Derived from Spatial Databases,” Geographical Analysis, Vol. 29, No.1, 1997, pp. 35-49. doi:10.1111/j.1538-4632.1997.tb00944.x

[40] J. Oksanen and T. Sarjakoski, “Error Propagation of DEM-Based Surface Derivatives,” Computers and Geosciences, Vol. 31, No. 8, 2005, pp. 1015-1027. doi:10.1016/j.cageo.2005.02.014

[41] P. Goovaerts, “Geostatistics for Natural Resources Evaluation (Applied Geostatistics),” Oxford University Press, New York, 1997.

[42] A. Temme, G. Heuvelink, J. Schoorl and L. Claessens, “Geostatistical Simulation and Error Propagation in Geomorphometry,” In: T. Hengl and H. I. Reuter, Eds., Geomorphometry: Concepts, Software, Applications, Developments in Soil Science, Elsevier, Berlin, 2008, pp 121- 140.

[43] G. B. M. Heuvelink, “Error Propagation in Environmental Modelling with GIS,” Taylor & Francis, London, 1998.

[44] E. J. Pebesma, “Multivariable Geostatistics in S: The Gstat Package,” Computer and Geosciences, Vol. 30, No.7, 2004, pp. 683-691. doi:10.1016/j.cageo.2004.03.012

[45] O. Planchon and F. Darboux, “A Fast, Simple and Versatile Algorithm to Fill the Depressions of Digital Elevation Models,” Catena, Vol. 46, No. 2, 2001, pp. 159-176. doi:10.1016/S0341-8162(01)00164-3

[46] J. P. Ribeiro and P. J. Diggle, “Package ‘geoR’: Analysis of Geostatistical Data,” R Package Version 1.6-35, 2011.

[47] J. N. Lewin-Koh and R. Bivand, “Package ‘Maptools’: Tools for Reading and Handling Spatial Objects,” R Package Version 0.8-10, 2011.

[48] A. Brenning, “Package ‘RSAGA’: SAGA Geoprocessing and Terrain Analysis in R,” R Package Version 0.92-2, 2011.

[49] A. Brenning, “RPyGeo: ArcGIS Geoprocessing in R via Python,” R Package Version 0.9-0, 2011.

[50] T. Hengl, G. B. M. Heuvelink and E. E. Van Loon, “On the Uncertainty of Stream Network Derived from Elevation Data: The Error Propagation Approach,” Hydrology and Earth Sciences Discussions, Vol. 14, No. 7, 2010, pp. 767-799. doi:10.5194/hessd-7-767-2010