Defining modern day Area-Altitude Balance Ratios (AABRs) and their use in glacier-climate reconstructions

With the increasing use of digital elevation models in palaeo-glacier reconstructions and the availability of freeware spreadsheets the Area-Altitude Balance Ratio (AABR) and Balance Ratio (BR) methods are becoming increasingly used in palaeo-glacier reconstruction for estimating Equilibrium Line Altitudes (ELA) and subsequently deriving quantitative estimates of palaeo-climate. While there are many data detailing contemporary Accumulation Area Ratios, there are still only a few studies that have established, from contemporary environments, AABR/BR ratios. Publicly available glacier mass balance (World Glacier Monitoring Service, US Geological Survey, and Norwegian Water Directorate) and spatial extent datasets provided the basis for this research. From a time series of mass balance, regressing specific net balance against ELA allows the zero net balance ELA to be identified. Once the zero balance ELA is established, the glacier hypsometry above and below the ELA is defined. The AABR/BR is calculated by using (the right hand side) the following: AABR=bnab/bnac=(z¯acAac)/(z¯abAab), where, bnab and bnac   are the net mass balance gradients in the ablation and accumulation zones respectively, z¯ac and z¯ab are the area-weighted mean altitudes of the accumulation and ablation areas respectively and Aac and Aab are the areas of the accumulation and ablation areas respectively. AABRs are calculated for a suite of glaciers located across a range of climatic zones and glacier types, with Antarctica being excluded. The following “representative” AABRs are found: a global AABR = 1.75 ± 0.71; Mid-latitude maritime = 1.9 ± 0.81; High-latitude = 2.24 ± 0.85; North America – West Coast = 2.09 ± 0.93; North America – Eastern Rockies = 1.11 ± 0.1; Canadian Arctic = 2.91 ± 0.35; Svalbard = 2.13 ± 0.52; Western Norway = 1.5 ± 0.4; European Alps = 1.59 ± 0.6; Central Asia = 1.75 ± 0.56; Kamchatka = 3.18 ± 0.16. This study provides an empirically derived dataset characterising AABR ratios which may be used for ELA estimation in palaeo-glacier reconstructions and for palaeo-climate quantification.