An adaptive-grid finite-volume model of glacier-terminus fluctuations

An adaptive-grid finite-volume glacier model is described. The model is an implicit one-dimensional flowline model. The discretized implicit finite-volume equations are solved by an iterative predictor–corrector method. The grid adapts as the terminus moves in response to changes in surface mass balance. Only the terminus grid point and the penultimate grid point are adapted as the glacier-terminus position changes in order to minimize computation. Several modelling experiments are carried out to demonstrate the performance of the model. Comparisons are made with a fixed-grid finite-volume model and a fixed-grid finite-difference model. Comparisons are made on two levels. The differences in methods, finite-volume method versus finite-difference method, arise from differences in accuracy and programming efficiency. The differences in grids, adaptive-grid versus fixed-grid, arise from differences in the numerical smoothness of the motion of the moving terminus. This affects questions of stability and accuracy.