Response time of glaciers as a function of size and mass balance: 2. Numerical experiments

Numerical experiments were made using a time-dependent nonlinear finite element model of glacier flow to seek confirmation of theoretical predictions made in the companion to this paper [Bahr et al., this issue]. The theoretical analysis indicates that under conditions of equal gradients in mass balance along the glacier surface (partial derivative(b) over dot/partial derivative x), other variables being held constant, response time to mass balance perturbations will decrease as glacier size increases. This behavior is confirmed by the numerical model experiments, which are performed on a suite of 23 radially symmetric ice caps with sizes ranging over similar to 4 orders of magnitude. The shape and mass balance profiles of the ice caps are defined so that partial derivative(b) over dot/partial derivative x is constant over all ice caps, and for uniform perturbations in mass balance, the modeled response times are faster for larger ice caps. The model results also confirm a volume/area scaling relationship established in the theoretical discussion and confirm the equivalence between two measures of response time, one arising from the present theory and the other a conventional expression of response time. The apparent discrepancy between the present results and preexisting theory is discussed, and it is shown that the results are compatible.