Hydrologic control of sliding velocity in two Alaskan glaciers : observation and theory
Short term variations in the velocities of glaciers reflect changes in the processes which determine sliding velocity. The role of water in these processes is considered for certain types of variable behavior observed on two glaciers in Alaska. Pulses of increased velocity on Variegated Glacier (...
| Summary: | Short term variations in the velocities of glaciers reflect changes in the processes which determine sliding velocity. The role of water in these processes is considered for certain types of variable behavior observed on two glaciers in Alaska.
Pulses of increased velocity on Variegated Glacier (mini-surges) prior to its 1982-83 surge have been attributed to pulses of water at the glacier bed. Our field program in 1986 demonstrated that mini-surges still occurred following the surge; the propagation of two such disturbances over part of the upper reach of the glacier was documented. The mini-surges of 1986 had substantially lower peak velocities but only slightly lower propagation velocities than the pre-surge mini-surges. The first of the mini-surges observed in 1986 originated in the tributary, the second originated in the upper reach of the main glacier.
A model of the basal water system with pressure dependent conductivity and storage is developed to investigate the conditions necessary for propagation of a pulse of water. The response of this system to the introduction of a localized increase in input is followed with a finite difference formulation. The extra input of water produces a downglacier propagating front, which, for reasonable values of porosity and pre-event conditions, moves at speeds similar to those observed for mini-surges.
The relation between the non-linearity of the pressure dependence in this model and the shape and history of the propagating disturbances is investigated using conductivity relations which have linear, quadratic, and cubic dependence on pressure, and one with an inverse dependence on the effective pressure. The modeling indicates that a system with a non-linear change of conductivity in response to a change in water pressure (suggestive of a cavity system) is required to match the field observations.
The shapes of waves which propagate with unchanging form in this system can be found theoretically; the numerical model generates these waves when the input rate is held constant. The constant form shapes are calculated for the conductivity relations mentioned above; for conductivities with higher-than-linear dependence on pressure the waves reach a plateau upglacier; the linear case increases without bound.
Modeling of a Rothlisberger tunnel system with the addition of a storage term indicates that such a system will propagate a disturbance, but will not match the abrupt rise times seen in boreholes as a mini-surge wave passes. The pressure dependent conductivity model does a better job of matching observations.
Columbia Glacier, a large tidewater glacier in southern Alaska, experiences noteworthy velocity fluctuations during the melt season in response to storms and increased ablation, and also displays a well developed diurnal cycle in velocity. A 1987 field project involving the University of Colorado, tbe USGS, and Caltech collected detailed time series of surface velocity, water input and discharge, and basal water pressure. These data show a complex pattern of behavior which is highly correlated with variations in hydrologic parameters. Basal water pressures near the floatation level are related to the rapid surface motion (4-8 m/d) of this glacier. A series of at least four velocity events accompanied elevated inputs of water to the glacier. These speed-ups did not have a strong coincident peak in basal water pressure, but were followed by an increase in outflow discharge from the glacier.
An estimate of the change in the volume of water stored in the glacier is made by relating input to the glacier (estimated from the filling rate of an ice-marginal lake and also from meteorological records) to discharge. This calculation shows that variations in velocity on time scales longer than one day can be explained by changes in the volume of water stored in or under the ice. The first velocity event was followed by a slowdown of the glacier which was coincident with a drop in stored water volume of about 0.1 m3/m2 averaged over the ice surface. The peak in velocity for the largest velocity event is accompanied by a large peak in stored water volume.
A model of the basal water system which consists of co-existing linked cavity and tunnel components is proposed to explain the melt season behavior of Columbia Glacier. In this hybrid cavity/tunnel system the distributed input of water reaches the bed and flows through the cavities to reach large tunnels which are responsible for the downglacier transport of water. The cavity part of this system is responsible for the correlation between stored water volume and velocity, while the tunnel system is responsible for the seasonal variation of velocity and the localized upwelling of water discharged from the terminus of the glacier.
A model based on a simple sliding law, an effective pressure distribution at the bed which is determined by the discharge through a tunnel system, and continuity for the ice is used to look at the role of effective pressure in the difference between winter and summer glacier-flow behavior. This model produces the late-melt-season pulse in velocity at the terminus which is related to an annual increase in calving rate. This may explain the previously discovered correlation between calving rate and outflow discharge, as well as the connection between the location of calving activity and the location of upwelling at the terminus.
The results of this work suggest that the complicated behavior of these glaciers can be understood at a simple level from the variations in hydrologic systems.
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