Correction to Variations of Ice Bed Coupling Beneath and Beyond Ice Streams: The Force Balance

A geometrical force balance that links stresses to ice bed coupling along a flow band of an ice sheet was developed in 1988 for longitudinal tension in ice streams and published 4 years later. It remains a work in progress. Now gravitational forces balanced by forces producing tensile, compressive, basal shear, and side shear stresses are all linked to ice bed coupling by the floating fraction phi of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how phi varies along these flow bands where surface and bed topography are known: phi = h(O)/h(I) with h(O) being ice thickness h(I) at x = 0 for x horizontal and positive upslope from grounded ice margins. This captures the basic fact in glaciology: the height of ice depends on how strongly ice couples to the bed. It shows how far a high convex ice sheet (phi = 0) has gone in collapsing into a low flat ice shelf (phi = 1). Here phi captures ice bed coupling under an ice stream and h(O) captures ice bed coupling beyond ice streams.

The Response of a Small Stream in the Lesni Potok Forested Catchment, Central Czech Republic, to a Short-Term In-Stream Acidification

Lesni Potok stream drains a forested headwater catchment in the central Czech Republic. It was artificially acidified with hydrochloric acid (HCl) for four hours to assess the role of stream substrate in acid-neutralisation and recovery. The pH was lowered from 4.7 to 3.2. Desorption of Ca and MP and desorption or solution of Al dominated acid-neutralisation; Al mobilisation was more important later. The stream substrate released 4.542 meq Ca, 1, 184 meq Mg, and 2,329 meq Al over a 45 in long and I in wide stream segment, smaller amounts of Be. Cd, Fe, and Mn were released. Adsorption of SO42- and desorption of F- occurred during the acidification phase of the experiment. The exchange reactions were rapidly reversible for Ca, Mg and SO42- but not symmetric as the substrate resorbed 1083, 790 and 0 meq Ca, Mg, and Al. respectively, in a 4-hour recovery period. Desorption of SO42- occurred during the resorption of Ca and Mg. These exchange and dissolution reactions delay acidification, diminish the pH depression and retard recovery from episodic acidification. The behaviour of the stream substrate-water interaction resembles that for soil-soil water interactions. A mathematical dynamic mass-balance based model, MASS (Modelling Acidification of Stream Sediments), was developed which simulates the adsorption and desorption of base cations during the experiment and was successfully calibrated to the experimental data.

Glacier Calving: A Numerical Model of Forces in the Calving-Speed/Water-Depth Relation

Empirical data suggest that the race of calving of grounded glaciers terminating in water is directly proportional to the water depth. Important controls on calving may be the extent to which a calving face tends to become oversteepened by differential flow within the ice and the extent to which bending moments promote extrusion and bottom crevassing at the base of a calving face. Numerical modelling suggests that the tendency to become oversteepened increases roughly linearly with water depth. In addition, extending longitudinal deviatoric stresses at the base of a calving face increase with water depth. These processes provide a possible physical explanation for the observed calving-rate/water-depth relation.

Geometrical Force Balance in Glaciology

The analytical force balance traditionally used in glaciology relates gravitational forcing to ice surface slope for sheet flow and to ice basal buoyancy for shelf flow. It is unable to represent stream flow as a transition from sheet flow to shelf flow by having gravitational forcing gradually passing from being driven by surface slope to being driven by basal buoyancy downslope along the length of an ice steam. This is a serious defect, because ice streams discharge up to 90% of ice from ice sheets into the sea. The defect is overcome by using a geometrical force balance that includes basal buoyancy, represented by the ratio of basal water pressure to ice overburden pressure, as a source of gravitational forcing. When combined with the mass balance, the geometrical force balance provides a holistic approach to ice flow in which resistance to gravitational flow must be summed upstream from the calving front of an ice shelf. This is not done in the analytical force balance, and it provides the ice-thinning rate required by gravitational collapse of ice sheets as interior ice is downdrawn by ice streams.