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A three-dimensional flow model of a firn-covered, cold glacier is developed with emphasis on the firn compressibility. The model proves to be very successful in calculating the age-depth relation of several ice cores drilled on Colle Gnifetti, Monte Rosa, Swiss Alps. The compressibility of firn is taken into account by appropriate constitutive equations which are implemented in two finite element codes. A flow law parameterization proposed by Gagliardini and Meysonnier (1997) is used throughout this study.
Ice thicknesses of Colle Gnifetti have been measured with radio echo soundings and are interpreted with digital signal processing and seismic migration techniques. The resulting ice thicknesses match borehole depths within the accuracy of the method. Measurements of borehole temperatures, surface velocities and accumulation rates provide the basis for glacier flow models in two and three dimensions. Firn density and englacial temperatures are either prescribed or calculated in coupled models. Measured surface velocities, density profiles, the ages of chemically dated layers in ice cores and the closure of a 100m deep borehole provide benchmarks for the models. The good agreement of modeled and measured quantities corroborates that the models include the relevant physical processes and particularly that the firn flow law is well suited for this type of glaciers. This study provides new constraints on the age of the basal ice as well as the source regions of the ice cores. An exceptional flow behaviour of the basal ice layer was detected in measurements of borehole closure and inclination. Measured deformation rates exceed upper bounds derived from the flow models and are thus attributed to altered rheological properties. Marked bends observed in the temperature profiles from two recent boreholes are interpreted with help of a transient heat flow model, driven with a temperature history. The conclusion is that substantial warming of the mean firn surface temperature has taken place over the last decades. This has not been observed so far in cold firn regions of the Alps. Modeled heat fluxes in the massif of Monte Rosa are strongly influenced by topographic effects, leading to a spatial variability of the temperature gradient near the glacier base. Such a variation has been observed in deep boreholes. These model results rely on the assumption of an extremely low vertical heat flux at depth. Driving the transient heat flow model with the temperature history since the last ice age shows, that this is merely a paleoclimatic effect, possibly enhanced by a degrading permafrost base.
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