A first-order flexible ELA model based on geomorphic constraints

Alpine glaciers, with their valuable combination of highly sensitive response to climate and near-global extent, are powerful tools for investigating previous and present climate changes. They also represent critical water resources for areas around the globe, with the potential for far-reaching effects in a warming world. Advancements to understand and model glacial changes and the variables influencing them are therefore paramount. Many glacier models fall into one of two endmembers: either highly complex transient models requiring careful tuning of multiple parameters to individual glaciers, or basic empirical correlations of glacier area and length with few considerations for local and regional variations in characteristics. Here we detail a physical steady-state model for alpine glaciers relating directly to glacier mass balance (via the equilibrium line altitude) while retaining the simplicity of other morphology methods, and simultaneously including error estimates. We provide custom MATLAB functions as a user-friendly and generally-applicable method to estimate glacier equilibrium line altitudes from only a limited number of glacier bed topography and glacier width measurements. As a test of the model's efficacy, we compare the model results for present-day glaciers in the Swiss Alps with previously published estimates of equilibrium line altitudes and intermediate model outputs.•The method estimates glacier equilibrium line altitudes from a limited set of bed topography measurements and constraints on glacier width.•The method is based on continuity equations, reducing the need for empirical coefficients tuned with measured data.•The method uses Monte Carlo sampling and bootstrapping to generate uncertainty bounds on the equilibrium line altitude estimates.