Response of valley glaciers to climate change and kinematic waves: a study with a numerical ice-flow model

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Abstract
A simple numerical flow model that couples mass divergence directly to basal shear stress as the only driving force is used to study kinematic waves. Kinematic waves that result from a perturbation of the ice thickness or mass balance are compared with the linear kinematic-wave theory of Nye/Weertman. The wave velocity is calculated as a function of the wavelength and amplitude of a perturbation. The modelled wave velocity is typically 6–8 times the vertically averaged velocity in the flow direction whereas linear theory predicts a factor of only 5. An experiment with the geometry of Hintereisferner, Austria, shows that the increase in the local ice velocity during a kinematic wave is about 10% but varies slightly depending on the position along the glacier and the amplitude of the kinematic wave. Kinematic waves are thus hard to detect from velocity measurements. The dynamics of simple continuity models are rich enough to support a variety of kinematic-wave phenomena. Such models are a useful tool to study the response of valley glaciers to climate change.

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