Abstract
Abstract. Volume–area scaling is the most popular method for estimating the ice volume of large glacier samples. Here, a series of resampling experiments based on different sets of synthetic data is presented in order to derive an upper-bound estimate (i.e. a level achieved only within ideal conditions) for its accuracy. For real-world applications, a lower accuracy has to be expected. We also quantify the maximum accuracy expected when scaling is used for determining the glacier volume change, and area change of a given glacier population. A comprehensive set of measured glacier areas, volumes, area and volume changes is evaluated to investigate the impact of real-world data quality on the so-assessed accuracies. For populations larger than a few thousand glaciers, the total ice volume can be recovered within 30% if all data currently available worldwide are used for estimating the scaling parameters. Assuming no systematic bias in ice volume measurements, their uncertainty is of secondary importance. Knowing the individual areas of a glacier sample for two points in time allows recovering the corresponding ice volume change within 40% for populations larger than a few hundred glaciers, both for steady-state and transient geometries. If ice volume changes can be estimated without bias, glacier area changes derived from volume–area scaling show similar uncertainties to those of the volume changes. This paper does not aim at making a final judgement on the suitability of volume–area scaling as such, but provides the means for assessing the accuracy expected from its application.
Highlights
Measuring the total ice volume of a glacier is virtually impossible
A number of contributions have addressed the topic, presenting a wide range of approaches with differing levels of complexity: methods that include direct ice thickness measurements have been presented by Fischer (2009), Morlighem et al (2011), McNabb et al (2012) and Farinotti et al (2013); the approach by Clarke et al (2009) is based on artificial neural networks, whilst several methods rely on principles of the ice dynamics (e.g. Raymond and Gudmundsson, 2009; Farinotti et al, 2009a; Linsbauer et al, 2012), with implementations ranging from the shallow-ice approximation (Li et al, 2011) to the Stokes formulation (Michel et al, 2013)
The accuracy that can be expected when using volume– area scaling for estimating the total volume, the total volume change, or the total area change of a glacier population was investigated using a series of resampling experiments
Summary
Measuring the total ice volume of a glacier is virtually impossible. Even with very detailed surveys of the ice thickness, which have recently been carried out for individual glaciers (e.g. King et al, 2009; Gabbi et al, 2012), the total ice volume needs to be recovered through interpolation of locally confined measurements. Raymond and Gudmundsson, 2009; Farinotti et al, 2009a; Linsbauer et al, 2012), with implementations ranging from the shallow-ice approximation (Li et al, 2011) to the Stokes formulation (Michel et al, 2013) Despite this wealth of approaches, many studies – especially those focusing on sea level change, mountain hydrology, and other climate change impacts – have been using, and still use, simpler approaches, mostly based on empirical relations between glacier volume and area The individual experiments are presented hereafter in different stand-alone sections in which the used data, the methods, and results are presented in succession with the aim of facilitating the reading
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