Abstract

Abstract. The surface mass balance (SMB) of a glacier provides the link between the glacier and the local climate. For this reason, it is intensively studied and monitored. However, major efforts are required to determine the point SMB at a sufficient number of locations to capture the heterogeneity of the SMB pattern. Furthermore, because of the time-consuming and costly nature of these measurements, detailed SMB measurements are carried out on only a limited number of glaciers. In this study, we investigate how to accurately determine the SMB in the ablation zone of Vadret da Morteratsch and Vadret Pers (Engadin, Switzerland) using the continuity equation method, based on the expression of conservation of mass for glacier flow with constant density. An elaborate dataset (spanning the 2017–2020 period) of high-resolution data derived from unoccupied aerial vehicle (UAV) measurements (surface elevation changes and surface velocities) is combined with reconstructed ice thickness fields (based on radar measurements). To determine the performance of the method, we compare modelled SMB with measured SMB values at the position of stakes. Our results indicate that with annual UAV surveys, it is possible to obtain SMB estimates with a mean absolute error smaller than 0.5 m of ice equivalent per year. Yet, our study demonstrates that to obtain these accuracies, it is necessary to consider the ice flow over spatial scales of several times the local ice thickness, accomplished in this study by applying an exponential decay filter. Furthermore, our study highlights the crucial importance of the ice thickness, which must be sufficiently well known in order to accurately apply the method. The latter currently seems to complicate the application of the continuity equation method to derive detailed SMB patterns on regional to global scales.

Highlights

  • The surface mass balance of a glacier is determined by the processes adding mass to the surface and those removing mass from the surface

  • mean absolute error (MAE) between measured and modelled elevation is on the order of a few centimetres (Table 2), which is similar to values found in other studies (Whitehead et al, 2013; Immerzeel et al, 2014; Wigmore and Mark, 2017; Zhang et al, 2019)

  • The small MAE and root mean square error (RMSE) of the digital surface model (DSM) in 2020 highlight the advantage of using an RTK equipped with an RTK GPS (P4RTK) for which a smaller number of ground control points (GCPs) are needed to reach similar or better accuracies compared to a classic set-up (UAV without RTK correction)

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Summary

Introduction

The surface mass balance of a glacier is determined by the processes adding mass to the surface (e.g. snowfall, freezing rain) and those removing mass from the surface (e.g. snow and ice melt, sublimation) These processes are strongly driven by the energy budget and precipitation over the glacier. A stake and snow pit network is used to determine the SMB followed by an interpolation and extrapolation to obtain the glacier mean specific mass balance (Braithwaite, 2002). This can result in large errors for glaciers where the heterogeneity of the SMB cannot be captured sufficiently by the available mea-

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