HESS Hydrology and Earth System Sciences HESS Hydrol. Earth Syst. Sci. 1607-7938 Copernicus Publications Göttingen, Germany 10.5194/hess-14-1153-2010 On the uncertainty of stream networks derived from elevation data: the error propagation approach Hengl T. 1 Heuvelink G. B. M. 2 van Loon E. E. 1 Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands Wageningen University and Research, P.O. Box 47, 6700 AA Wageningen, The Netherlands 02 07 2010 14 7 1153 1165 Copyright: © 2010 T. Hengl et al. 2010 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://hess.copernicus.org/articles/14/1153/2010/hess-14-1153-2010.html The full text article is available as a PDF file from https://hess.copernicus.org/articles/14/1153/2010/hess-14-1153-2010.pdf

DEM error propagation methodology is extended to the derivation of vector-based objects (stream networks) using geostatistical simulations. First, point sampled elevations are used to fit a variogram model. Next 100 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 method is illustrated using two small data sets: Baranja hill (30 m grid cell size; 16 512 pixels; 6367 sampled elevations), and Zlatibor (30 m grid cell size; 15 000 pixels; 2051 sampled elevations). All computations are run in the open source software for statistical computing R: package geoR is used to fit variogram; package gstat is used to run sequential Gaussian simulation; streams are extracted using the open source GIS SAGA via the RSAGA library. The resulting stream error map (Information entropy of a Bernoulli trial) clearly depicts areas where the extracted stream network is least precise – usually areas of low local relief and slightly convex (0–10 difference from the mean value). In both cases, significant parts of the study area (17.3% for Baranja Hill; 6.2% for Zlatibor) show high error (<I>H</I>&gt;0.5) of locating streams. By correlating the propagated uncertainty of the derived stream network with various land surface parameters sampling of height measurements can be optimized so that delineated streams satisfy the required accuracy level. Such error propagation tool should become a standard functionality in any modern GIS. Remaining issue to be tackled is the computational burden of geostatistical simulations: this framework is at the moment limited to small data sets with several hundreds of points. Scripts and data sets used in this article are available on-line via the <a href="www.geomorphometry.org" target="_blank">www.geomorphometry.org</a> website and can be easily adopted/adjusted to any similar case study.

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