Topographic uncertainty quantification for flow-like landslide models via stochastic simulations

Digital elevation models (DEMs) representing topography are an essential input for computational models capable of simulating the run-out of flow-like landslides. Yet, DEMs are often subject to error, a fact that is mostly overlooked in landslide modeling. We address this research gap and investigate the impact of topographic uncertainty on landslide run-out models. In particular, we will describe two different approaches to account for DEM uncertainty, namely unconditional and conditional stochastic simulation methods. We investigate and discuss their feasibility, as well as whether DEM uncertainty represented by stochastic simulations critically affects landslide run-out simulations. Based upon a historic flow-like landslide event in Hong Kong, we present a series of computational scenarios to compare both methods using our modular Python-based workflow. Our results show that DEM uncertainty can significantly affect simulation-based landslide run-out analyses, depending on how well the underlying flow path is captured by the DEM, as well as on further topographic characteristics and the DEM error's variability. We further find that, in the absence of systematic bias in the DEM, a performant root-mean-square-error-based unconditional stochastic simulation yields similar results to a computationally intensive conditional stochastic simulation that takes actual DEM error values at reference locations into account. In all other cases the unconditional stochastic simulation overestimates the variability in the DEM error, which leads to an increase in the potential hazard area as well as extreme values of dynamic flow properties.

Topographic uncertainty quantification for flow-like landslide models via stochastic simulations

Topography representing digital elevation models (DEMs) are essential inputs for computational models capable of simulating the run-out of flow-like landslides. Yet, DEMs are often subject to error, a fact that is mostly overlooked in landslide modeling. We address this research gap and investigate the impact of topographic uncertainty on landslide-run-out models. In particular, we will describe two different approaches to account for DEM uncertainty, namely unconditional and conditional stochastic simulation methods. We investigate and discuss their feasibility, as well as whether DEM uncertainty represented by stochastic simulations critically affects landslide run-out simulations. Based upon a historic flow-like landslide event in Hong Kong, we present a series of computational scenarios to compare both methods using our modular Python-based workflow. Our results show that DEM uncertainty can significantly affect simulation-based landslide run-out analyses, depending on how well the underlying flow path is captured by the DEM, as well as further topographic characteristics and the DEM error's variability. We further find that in the absence of systematic bias in the DEM, a performant root mean square error based unconditional stochastic simulation yields similar results than a computationally intensive conditional stochastic simulation that takes actual DEM error values at reference locations into account. In all other cases the unconditional stochastic simulation overestimates the variability of the DEM error, which leads to an increase of the potential hazard area as well as extreme values of dynamic flow properties.

Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset

Digital elevation models (DEMs) are a gridded representation of the surface of the Earth and typically contain uncertainties due to data collection and processing. Slope and aspect estimates on a DEM contain errors and uncertainties inherited from the representation of a continuous surface as a grid (referred to as truncation error; TE) and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect. Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics and to compare calculations on DEMs of different sizes and accuracies. Using lidar data with point density of ∼10 pts m−2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the 1 m dataset are on average 0.3∘ (0.9∘) from TE and 5.5∘ (14.5∘) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of 4 m that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the 4 m DEM are 0.25∘ (0.75∘) from TE and 5∘ (12.5∘) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.

Determining the Optimal Grid Resolution for Topographic Analysis on an Airborne Lidar Dataset

Digital Elevation Models (DEMs) are a gridded representation of the surface of the earth and typically contain uncertainties due to data collection and processing. The topographic metrics slope and aspect contain errors and uncertainties inherited both from the representation of a continuous surface as a grid (referred to as truncation error, TE), and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect. Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics, and to compare calculations on DEMs of different sizes and accuracies. Using lidar data with point density of ~ 10 pts/m2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the one-meter dataset are on average 0.3° (0.9°) from TE, and 5.5° (14.5°) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of four meters that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the four meter DEM are 0.25° (0.75°) from TE and 5° (12.5°) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.

Visualising DEM-related flood-map uncertainties using a disparity-distance equation algorithm

The apparent absoluteness of information presented by crisp-delineated flood boundaries can lead to misconceptions among planners about the inherent uncertainties associated in generated flood maps. Even maps based on hydraulic modelling using the highest-resolution digital elevation models (DEMs), and calibrated with the most optimal Manning's roughness (n) coefficients, are susceptible to errors when compared to actual flood boundaries, specifically in flat areas. Therefore, the inaccuracies in inundation extents, brought about by the characteristics of the slope perpendicular to the flow direction of the river, have to be accounted for. Instead of using the typical Monte Carlo simulation and probabilistic methods for uncertainty quantification, an empirical-based disparity-distance equation that considers the effects of both the DEM resolution and slope was used to create prediction-uncertainty zones around the resulting inundation extents of a one-dimensional (1-D) hydraulic model. The equation was originally derived for the Eskilstuna River where flood maps, based on DEM data of different resolutions, were evaluated for the slope-disparity relationship. To assess whether the equation is applicable to another river with different characteristics, modelled inundation extents from the Testebo River were utilised and tested with the equation. By using the cross-sectional locations, water surface elevations, and DEM, uncertainty zones around the original inundation boundary line can be produced for different confidences. The results show that (1) the proposed method is useful both for estimating and directly visualising model inaccuracies caused by the combined effects of slope and DEM resolution, and (2) the DEM-related uncertainties alone do not account for the total inaccuracy of the derived flood map. Decision-makers can apply it to already existing flood maps, thereby recapitulating and re-analysing the inundation boundaries and the areas that are uncertain. Hence, more comprehensive flood information can be provided when determining locations where extra precautions are needed. Yet, when applied, users must also be aware that there are other factors that can influence the extent of the delineated flood boundary.