Mc k0exp[T T0Tc HH w10

where HW is the water depth, H is the ice thickness and T is ice temperature. The parameters k0, T0 and Tc establish calving vigour and the reduction in calving rates with decreasing temperature. The value for T0 is typically set to 273.16K, such that calving rates are maximal for isothermal ice (T = 273.16K; mc = k0HHW) and mc exponentially decreases for colder ice. This crudely mimics the difference in calving rates observed in mid-latitude tidewater environments versus polar environments, where calving rates are low enough to permit ice-shelf development.

This calving model permits floating/shelf ice to expand over the continental shelf or shelf break, but it is not necessarily closer or dV = HdA (Johannesson et al., 1989; Harrison et al., 2001).

With this assumption, Harrison et al. (2001) consider the long-term volume response of an ice mass to a change in mass balance with respect to an initial 'reference' geometry (elevation and area distribution). This provides a framework for explicit consideration of the effects of changing surface elevation as a glacier responds to climatic changes. Harrison et al. (2001) introduce these effects through the parameter G (z) = db(z)/dz, which represents the vertical mass balance gradient (see also Elsberg et al., 2001). An effective glacier-wide vertical mass balance gradient, Ge, is calculated through a weighted averaged of G (z) over the ice mass. The predicted volume response time to a mass balance perturbation, tV, can then be estimated from

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