Identifying LiDAR sample uncertainty on terrain features from DEM simulation

Abstract

Light detection and ranging (LiDAR) is an effective technology to detect highly dense-point elevation data from terrain surfaces. The density of LiDAR data points significantly affects the level of detail of a high-resolution digital elevation model (DEM). In this study, the conditioned Latin hypercube sampling (cLHS) and simple random sampling (SRS) methods select sufficient LiDAR samples, and sequential Gaussian simulation (SGS) generates multiple DEM realizations that are a set of simulated DEM maps subject to a specified mean, variance, and spatial structure of measured data. Based on DEM realizations, the uncertainty of a spatial feature with a specified elevation is determined.

The results suggest that LiDAR sampling patterns, including the size and configuration, affect the spatial distribution of the feature uncertainty, especially when the sample size is small. The accuracy of a DEM is dependent on the choice of sampling techniques for low sampling density data. Unlike random sampling, the cLHS method replicates the distribution of spatial elevation patterns in small sample sizes. Hence, the integrated method can assess the uncertainty of spatial features efficiently in geomorphic monitoring and management.

Introduction

A raster DEM (digital elevation model) is a pixel-based representation of topography as a function of spatial location (Yue et al., 2007). LiDAR (light detection and ranging) has recently emerged as a crucial technology for high-resolution DEM generation. LiDAR is an optical remote sensing approach in which scattered light properties are measured to determine the range and other information of an object (Guo et al., 2010). Detailed high-resolution DEMs can be generated based on high-density LiDAR data using appropriate interpolation methods (Liu et al., 2007, Guo et al., 2010).

Numerous previous studies have applied a triangulated irregular network (TIN) and interpolation methods to investigate DEMs (Chaplot et al., 2006, Liu et al., 2007, Yue et al., 2007, Chen and Yue, 2010, Guo et al., 2010). Commonly used interpolation methods include inverse distance weighted (IDW), natural neighbor, spline, and geostatistical methodologies such as kriging and stochastic simulation. Stochastic simulation can preserve high spatial variability and local variability of data (Deutsch and Journel, 1998, Lin et al., 2001, Delbari et al., 2009, Chu et al., 2012). This study used stochastic simulation to obtain DEMs and identify the uncertainty of spatial features based on representative samples. The simulation approach can be used to generate multiple DEM realizations that are a set of simulated DEM maps subject to a specified mean, variance and spatial structure of measured data. Sequential Gaussian simulation (SGS) is a commonly used stochastic simulation algorithm (Fredericks and Newman, 1998). The simulation results match the sample statistics whereas the conditioning data provide a quantitative measure of spatial uncertainty (Chu et al., 2012). The uncertainty associated with spatial features observed in the DEM, such as the probability of the existence of an entire ridge, can be modeled from this set of simulated realizations. The uncertainty is usually associated with DEM errors (Hebeler and Purves, 2009). The three main sources of such DEM errors are as follows: (1) measurement and generation of source data; (2) data processing and DEM generation from sample data; and (3) the properties of the terrain surface modeled with respect to its representation in a DEM (Fisher and Tate, 2006, Hebeler and Purves, 2009). However, DEMs are often used in terrain analyses without quantifying the effect of the uncertainty.

Sampling is one of the main steps of LiDAR data processing. Sampling density has considerable influences on the accuracy of LiDAR-derived DEMs (Heritage et al., 2009, Milan and Heritage, 2012). Heritage et al. (2009) and Milan et al. (2011) identified the effects of sampling data densities and patterns on morphological investigations. Wheaton et al. (2010) estimated the DEM uncertainty and evaluated the consequences of geomorphic change for sediment budgeting improvement. The use of an insufficient density of samples may lead to a misrepresentation of the complexity of the terrain. A number of studies argued that Latin hypercube sampling (LHS) can be used to explore the parameter space of a model more extensively than simple random sampling (SRS) can (McKay et al., 1979, Xu et al., 2005, Hassan and Atkins, 2007, Post et al., 2008). LHS, a technique of stratified sampling, is more efficient than SRS for univariate distributions (McKay et al., 1979). LHS can be used to generate a set of samples and precisely represent the pattern of data distribution. Xu et al. (2005) integrated LHS and stochastic simulation in a forest landscape simulation model. Their results show that LHS can be used to capture more variability in the sample space than SRS, especially for a small number of simulations. Minasny and McBratney (2006) used conditioned Latin hypercube sampling (cLHS) with prior information to represent ancillary data of the Hunter Valley in New South Wales, Australia. The results showed that cLHS is more effective than SRS and stratified spatial sampling for replicating the distribution of variables. cLHS fully covers each variable by ensuring an excellent spread of sampling points and maximally stratifying the marginal distribution (Minasny and McBratney, 2006, Lin et al., 2010).

The main objective of this study was to investigate the LiDAR data sampling effect on high-resolution DEM uncertainty. The uncertainty of a spatial feature with a specified elevation was determined using the SGS with various LiDAR samples. The cLHS and SRS approaches were applied to select LiDAR data. Subsequently, SGS was used to generate multiple DEMs based on LiDAR samples. In a case study based on various sample sizes, the uncertainty pattern of a terrain feature was compared.