Uncertainty assessment of multi-temporal airborne laser scanning data: A case study on an Alpine glacier

Abstract

In glaciology, volumetric changes from multi-temporal digital elevation models (DEMs) serve to validate and calibrate glacier mass balances from traditional in situ measurements. In this study, we provide a thorough uncertainty assessment of multi-temporal airborne laser scanning DEMs based on: (a) applying a statistical error model, (b) comparing laser echoes to reference points and surfaces, and (c) developing a physical error propagation model. The latter model takes into account the measurement platform characteristics, components of the measurement process, and the surface properties. Such a model allows the estimation of systematic and stochastic uncertainties for single laser echoes, as well as for distributed surfaces in every part of the study site, independent of the reference surfaces. The full error propagation framework is applied to multi-temporal DEMs covering the highly undulating terrain in the Findelengletscher catchment in Canton Valais, Switzerland. This physical error propagation model is able to reproduce stochastic uncertainties in accordance with measurements from reference surfaces. The high laser point density in the study site reduces the stochastic uncertainties over the whole glacier area to negligibly small values. However, systematic uncertainties greatly influence the calculation of mass changes and lead to corrections of the thickness change of up to 35%.

Introduction

Since the 1990s, digital elevation models derived from airborne laser scanning (ALS) have been increasingly used for a wide range of applications (Shan & Toth, 2009). In the last decade, regional to nation-wide surveys have been carried out using ALS, including regions with potential relevance for glacier research, e.g. in Austria and Norway (Geist et al., 2003), and in Switzerland (Geist et al., 2003, Luethy and Stengele, 2005). As the costs associated with ALS are decreasing and the initial datasets are being updated, the prospect of multi-temporal ALS data will sustain new applications, not only in forestry (Yu et al., 2004) but also in natural hazards (Casas et al., 2011, Ventura et al., 2011). However, to make sure that these applications can be used best, new means of validation and uncertainty assessment will need to be implemented (Hopkinson et al., 2008), especially since ALS is a constantly evolving technology, and changing systems and/or survey configurations will result in different datasets with varying accuracies.

In the domain of glaciology, mass balance is traditionally measured in situ using ablation stakes and snow pits, including density measurements. Additionally, different methods are applied to inter-/extrapolate from discrete measuring locations to the entire glacier to calculate the so-called direct glaciological mass balance (cf. Østrem & Brugmann, 1991). To account for the possible accumulation of systematic errors from these seasonal or annual measurements, an independently derived geodetic mass balance at decadal intervals is required (Haug et al., 2009, Huss et al., 2009, Zemp et al., 2010). The standard geodetic method applied is digital elevation model (DEM) differencing from photogrammetric sources (e.g. Haug et al., 2009). However, photogrammetric DEM extraction is hindered by the low contrast often found in alpine environments. ALS has proved to be useful in overcoming the shortcomings of photogrammetric DEMs as it directly measures surface elevations (e.g. Geist, 2005, Kennett and Eiken, 1996).

Several studies have focused on the application of ALS to glacier surface mapping or volume changes (e.g. Abermann et al., 2009, Favey et al., 1999, Geist, 2005, Kennett and Eiken, 1996, Knoll and Kerschner, 2010). To date, ALS accuracy assessments have been conducted using reference surfaces (Favey et al., 1999, Geist, 2005), ground control points (Hodgson and Bresnahan, 2004, Hopkinson and Demuth, 2006) and theoretical or statistical error modeling approaches (Filin, 2003, Goulden and Hopkinson, 2010a, Huising and Gomes Pereira, 1998). In glaciology, stochastic uncertainties in airborne laser scanning DEMs are considered to be lower than other DEM-providing methods. In ALS, vertical accuracies are given between ±0.1 m and ± 0.3 m (Abermann et al., 2010). However, estimations of uncertainties are usually based on numbers from data providers or are measured using reference surfaces or points, and may therefore not cover stochastic uncertainties present at the study site (e.g. glacier) itself. Additionally, it is not always clear which scale these stochastic uncertainties refer to, i.e. whether they refer to a single measurement (e.g. single laser return), a single raster cell or even the stochastic uncertainty of a whole study site. Furthermore, systematic uncertainties in DEMs directly influence the effects of elevation changes, but are often not considered.

In this study, we developed and implemented a three-step approach to estimate both the systematic and the stochastic uncertainties in DEMs derived from ALS data. First, we checked for co-registration and elevation-dependent errors between each pair of DEMs. In a second step, we compared the location of single laser echoes to reference points and surfaces within the study site. Following this, we used a physical error propagation model to explain the uncertainties found in the previous method and attribute them to their sources. A validation of the physical error propagation model was carried out on reference surfaces and extended to the full point cloud of each ALS survey. Finally, we applied our framework to compute changes in glacier thickness from multi-temporal DEMs and to assess the related uncertainties statistically.