Hydrology and Earth System Sciences
On the uncertainty of stream networks derived from elevation data: the error propagation approach
T. Hengl1 , G. B. M. Heuvelink2 , and E. E. van Loon1
for Biodiversity andEcosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands 2 Wageningen University and Research, P.O. Box 47, 6700 AA Wageningen, The Netherlands Received: 22 December 2009 – Published in Hydrol. Earth Syst. Sci. Discuss.: 29 January 2010 Revised: 18 June 2010 – Accepted: 18 June 2010 – Published: 2 July 2010
Abstract. DEM error propagationmethodology 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 theerror 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 statisticalcomputing 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 (0–10difference 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 (H > 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. Sucherror 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 www.geomorphometry.org website and can be easily adopted/adjustedto any similar case study.
Correspondence to: T. Hengl (email@example.com)
In geomorphometry, Digital Elevation Models (DEM) are routinely used to extract various continuous (gridded) land surface parameters, and/or discrete (vector) land surface objects. Assuming that DEMs are perfectly accurate, extraction of land surface parameters and objects is a simple one iterationoperation (Fig. 1a). However, in reality, DEMs are not perfect representations of reality – DEMs suffer from systematic and random errors and DEM elevations differ from what we measure on the ﬁeld. In fact, errors are inevitable, even if elevation models are produced using highly accurate and dense sampling techniques such as LiDAR (Evans and Hudak, 2007; Bater and Coops, 2009). Errors are inherentboth in measurements of elevations, and in the DEM analysis algorithms, and can possibly have a signiﬁcant inﬂuence on the reliability of ﬁnal products. By ignoring errors in the input layers, analysts often get disappointed when their products are evaluated versus ground truth data. This is true especially for hydrological applications (Wise, 2000; Wechsler, 2007). The approach to GIS analysis...