Linear modeling of glacier fluctuations

In this contribution a linear first-order differential equation is used to model glacier length fluctuations. This equation has two parameters describing the physical characteristics of a glacier: the climate sensitivity, expressing how the equilibrium glacier length depends on the climatic state, and the response time, indicating how fast a glacier approaches a new equilibrium state after a stepwise change in the climatic forcing.Aprerequisite for the application of a linear model to a particular glacier is that length fluctuations over the period of interest are significantly smaller than the average length. The linear model is used to define and illustrate some concepts relevant to the study of glacier fluctuations. It is shown that glaciers are never in equilibrium with climate, and that a constant time lag between forcing and response cannot be expected. Next the linear glacier model is applied to real glaciers, showing how information on response times and a reconstruction of the climatic forcing can be extracted from length records. In the first application, two adjacent glaciers in the Oetztal Alps (Austria) are considered: Hintereisferner and Kesselwandferner. By optimizing the response times with a control method, reconstructed equilibrium-line histories for these glaciers are almost identical. The corresponding response times are 31 years for Hintereisferner, and only 2.1 years for Kesselwandferner. In the second application, four glacier length records from the Oberengadin (Switzerland) are used to reconstruct equilibrium-line histories. These appear to be mutually consistent, and the mean rise of the equilibrium line over the period 1894–2007 appears to be 1.4 m yr-1. An equilibriumline history derived from data of a nearby climate station yields about the same trend over this period, but shows significant differences on the decadal time scale.