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[1] We present a combined surface processes and tectonic model which allows us to determine the climatic and tectonic parameters that control the development of faceted spurs at normal fault scarps. Sensitivity tests to climatic parameter values are performed. For a given precipitation rate, when hillslope diffusion is high and channel bedrock is highly resistant to erosion, the scarp is smooth and undissected. When, instead, the bedrock is easily eroded and diffusion is limited, numerous channels develop and the scarp becomes deeply incised. Between these two end-member states, diffusion and incision compete to produce a range of scarp morphologies, including faceted spurs. The sensitivity tests allow us to determine a dimensionless ratio of erosion, f, for which faceted spurs can develop. This study evidences a strong dependence of facet slope angle on throw rate for throw rates between 0.4 and 0.7 mm/a. Facet height is also shown to be a linear function of fault throw rate. Model performance is tested on the Wasatch Fault, Utah, using topographic, geologic, and seismologic data. A Monte Carlo inversion on the topography of a portion of the Weber segment shows that the 5 Ma long development of this scarp has been dominated by a low effective precipitation rate ($1.1 m/a) and a moderate diffusion coefficient (0.13 m 2 /a). Results demonstrate the ability of our model to estimate normal fault throw rates from the height of triangular facets and to retrieve the average long-term diffusion and incision parameters that prevailed during scarp evolution using an accurate 2-D misfit criterion.

We first provide a critical review of statistical procedures employed in the literature for testing uncertainty in digital terrain analysis, then focus on several aspects of spatial autocorrelation that have been neglected in the analysis of gridded elevation data. When applied to first derivatives of elevation such as topographic slope, a spatial approach using Moran’s I and the LISA (Local Indicator of Spatial Association) allows: (1) georeferenced data patterns to be generated; (2) error hot- and coldspots to be located; and (3) error propagation during DEM manipulation to be evaluated. In a worked example focusing on the Wasatch mountain front, Utah, we analyse the relative advantages of six DEMs resulting from different acquisition modes (airborne, optical, radar, or composite): the LiDAR (2 m), CODEM (5 m), NED10 (10 m), ASTER DEM (15 m) and GDEM (30 m), and SRTM (90 m). The example shows that (apart from the LiDAR) the NED10, which is generated from composite data sources, is the least error-ridden DEM for that region. Knowing error magnitudes and where errors are located determines where corrections to elevation are required in order to minimize error accumulation or propagation, and clarifies how they might affect expert judgement in environmental decisions. Ground resolution issues can subsequently be addressed with greater confidence by resampling the preferred grid to terrain resolutions suited to the landscape attributes of interest. Source product testing is an essential yet often neglected part of DEM analysis, with many practical applications in hydrological modelling, for predictions of slope- to catchment-scale mass sediment flux, or for the assessment of slope stability thresholds.