Uncertainty assessment of multi-temporal airborne laser scanning data: A case study on an Alpine glacier
Highlights
► We investigate glacier thickness changes at a mountain glacier in Switzerland ► We produce multi-temporal airborne laser scanning digital elevation models ► Application of a stepwise accuracy assessment based on three methods ► Development and validation of a physical uncertainty propagation method ► Comparison of remote sensing glaciological results with in situ measurements
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.
Section snippets
Study site
The Findelengletscher is a temperate valley glacier located in the Swiss Alps (46° N, 7° 52′ E, Fig. 1) in Canton Valais, close to the village of Zermatt, Switzerland. With its area of more than 13 km2 and a length of about 6.7 km (2010), it is one of the larger valley-type glaciers in the Alps. Since its Little Ice Age maximum extent in c. 1850, when it was 10.4 km long and 19.96 km2 in area (Maisch et al., 2000), the glacier has retreated, interrupted by three shorter time periods of glacier
Interpolation of a point cloud into a raster
A preparatory step to facilitate data analysis is to interpolate the point clouds into raster models. For this task, a multitude of methods are at hand, e.g. inverse distance weighting or kriging (cf. Cressie, 1993). We converted the point clouds into 1 m x 1 m grids and used MATLAB (The MathWorks, Inc.) to delineate all points within a single raster cell and subsequently assign the average of all elevation values to provide the cell's elevation. This proved to be a very stable approach, as
Single DEM uncertainty assessment
Fig. 2 shows a visual and statistical comparison of discrete laser ground returns of 2009 with two perpendicular sections of a cross-gable roof (black lines). The laser point cloud is plotted with vertical error bars from error propagation results appended to each laser return. This representation allows the detection of systematic shifts in every direction. In addition to the positive vertical shift present on every rooftop surface, the residual difference between two surfaces sloping in
Uncertainties of the ALS point clouds and derived DEMs
The main contribution of this study is the development of a framework to assess systematic and stochastic uncertainties of ALS-derived DEMs in highly undulated terrain. Using reference points and surfaces from in situ surveys allowed a direct investigation of systematic as well as stochastic uncertainties. In order to explain the provenance of uncertainties, we developed a physical error propagation model for the ALS system. The results of this method show similar magnitudes of stochastic
Conclusion
We applied ALS in high mountain topography to assess glacier change based on differencing DEMs over a time period of five years as well as over one hydrological year. The corresponding winter and summer seasons were investigated separately. The well-defined setup of the ALS surveys, optimized for the glaciological purposes, and a homogenized post-processing resulted in high-precision DEMs. Furthermore, we were able to assess the stochastic and systematic uncertainty of the DEMs and resulting
Acknowledgements
We are grateful to Wilfried Haeberli and Michael Schaepman for their valuable support with this project. The authors acknowledge the hard work of the Findelengletscher field teams of the Universities of Fribourg and Zurich; without their combined effort, this project would not have been possible. We thank BSF Swissphoto for the acquisition of the ALS data and their continuous support. Many thanks to Silvia Dingwall for reviewing the language of the article. Urs Marti of swisstopo kindly
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