On the climate–geometry imbalance, response time and volume–area scaling of an alpine glacier: insights from a 3-D flow model applied to Vadret da Morteratsch, Switzerland

Abstract

AbstractA two-dimensional surface mass-balance model is coupled to a three-dimensional higher-order ice flow model to assess the imbalance between climate and glacier geometry for the Morteratsch (Engadine, Switzerland) glacier complex. The climate–geometry imbalance has never been larger than at present, indicating that the temperature increase is faster than the geometry is able to adapt to. We derive response times from transient and steady-state geometries and find that the volume response time is correlated to the magnitude of the mass-balance forcing. It varies between 22 and 43 years, while the length response time is between 47 and 55 years. Subsequently, the modelled response times are compared with different analytical methods from the literature. The effect of a climatic perturbation on the response time, which produces a spatially distributed mass-balance forcing, is also examined. We investigate the effect of glacier size on the response time and project that the response time will decrease in the future due to a surface steepening. Finally, volume–area scaling methods with different parameters are tested and an alternative method is proposed that takes into account the surface slope. The effect of a transient state on the method is also evaluated.