Initialization of a global glacier model based on present-day glacier geometry and past climate information: an ensemble approach

To provide estimates of past glacier mass changes over the course of the 20th century, an adequate initial state is required. However, empirical evidence about past glacier states at regional or global scales is largely incomplete, both spatially and temporally, calling for the use of automated numerical methods. This study presents a new way to initialize the Open Global Glacier Model from past climate information and present-day glacier states. We use synthetic experiments to show that even with these perfectly known but incomplete boundary conditions, the problem of model initialization is an ill-posed inverse problem leading to nonunique solutions, and we propose an ensemble approach as a way forward. The method works as follows: we generate a large set of physically plausible glacier candidates for a given year in the past (e.g., 1850 in the Alps), all of which are then modeled forward to the date of the observed glacier outline and evaluated by comparing the results of the forward runs to the present-day states. We test the approach on 2660 Alpine glaciers and determine error estimates of the method from the synthetic experiments. The results show that the solution is often nonunique, as many of the reconstructed initial states converge towards the observed state in the year of observation. We find that the median state of the best 5 % of all acceptable states is a reasonable best estimate. The accuracy of the method depends on the type of the considered observation for the evaluation (glacier length, area, or geometry). Trying to find past states from only present-day length instead of the full geometry leads to a sharp increase in uncertainty. Our study thus also provides quantitative information on how well the reconstructed initial glacier states are constrained through the limited information available to us. We analyze which glacier characteristics influence the reconstructability of a glacier, and we discuss ways to develop the method further for real-world applications.