Testing the area–altitude balance ratio (AABR) and accumulation–area ratio (AAR) methods of calculating glacier equilibrium-line altitudes

Rachel P Oien,Brice R Rea,Iestyn D Barr,Matteo Spagnolo,Robert G Bingham

doi:10.1017/jog.2021.100

Abstract

AbstractIn this study, we compare equilibrium-line altitudes (ELAs) calculated using the area–altitude balance ratio (AABR) and the accumulation–area ratio (AAR) methods, with measured ELAs derived from direct field observations. We utilise a GIS toolbox to calculate the ELA for 64 extant glaciers by applying the AABR and AAR methods to DEMs and polygons of their geometry. The calculated ELAs (c-ELAs) are then compared to measured zero-net balance ELAs (znb-ELAs) obtained from mass-balance time series held by the WGMS for the same glaciers. The correlation between znb-ELAs and AABR (1.56)/AAR (0.58) c-ELAs is very strong, with an r2 = 0.99. The smallest median difference between znb-ELAs and c-ELAs (i.e. 65.5 m) is obtained when a globally representative AABR of 1.56 is used. When applied to palaeoglacier-climate applications, this difference translates to ~0.42°C, well within the uncertainty of palaeotemperature proxies used to determine mean summer temperature at the ELA. The more widely used mean AABR of 1.75 is shown to be statistically invalid due to the skewness of the dataset. On this basis, when calculating glacier ELAs, we recommend the use of a global AABR value of 1.56.

Highlights

The results indicate that the global median area–altitude balance ratio (AABR) produces the smallest median difference between c-equilibrium-line altitudes (ELAs) and zero-net balance ELA (znb-ELA), but this is only marginally better than the area ratio (AAR) (0.58)
The first important result from this study relates to the frequency distribution analyses of the data used by Rea (2009) to generate the global mean AABR (Fig. 4)
The differences between calculated ELAs (c-ELAs) and znb-ELA, calculated using the global median AABR, are not normally distributed about the mean, so we report the absolute median difference between the two as 65.5 m

Summary

Introduction

Time series of ELAs may be analysed to track how glacier mass balance changes from year to year (WGMS, 2017). From these annual data, a climatically representative ELA can be calculated corresponding to the ELA averaged over a standard 30-year window (Sutherland, 1984; Rabatel and others, 2013) or the zero-net balance ELA (znb-ELA) can be calculated as the y-intercept value yielded through linear regression of a time series of annual specific net mass balance and ELA, which assumes the glacier is in equilibrium with climate (Rea, 2009)

Objectives

Methods

Conclusion