Fig. 1. A) Columbia Glacier, Alaska, June 2005. (W.T. Pfeffer, INSTAAR, University of Colorado at Boulder, USA. Image from the forthcoming book “Columbia Glacier at Mid-Retreat: The Opening of a New Landscape” to be published by American Geophysical Union. B) Ice front retreat, Columbia Glacier, 1978–2000. From Krimmel (2001).

Fig. 2. Variation of calving rate with water depth for tidewater and freshwater calving glaciers in different regions. From Haresign (2004).

Fig. 3. Schematic diagram of the three basic modes of fracturing.

Fig. 4. (A) Stress intensity factors (K(net)) and predicted crevasse depths for a fracture criterion of 0.1 MPa m^0.5 and applied tensile stresses of 100, 200, 300 and 400 kPa, using the Van der Veen (1998a) LEFM model. (B) Effect of crevasse spacing on modelled crevasse depth in the Van der Veen (1998a) model. Crevasse depth is less for closely-spaced crevasses because stress concentration effects are reduced. (C) Modelled crevasse depths for water level 8 m below the glacier surface, for crevasse spacings of 30, 40, 50 and 100 m.

Fig. 5. Pre-existing and new fractures at calving margins, Patagonia. (A) Glaciar Ameghino, December 1993; (B) Glaciar Upsala, east terminus, March 1993.

Fig. 6. (A) Hansbreen, Svalbard. (B) Velocity profiles from 1998 and 1999. The large differences in velocities between years reflects variations in basal hydrology. Adapted from Vieli et al. (2004).

Fig. 7. MODIS image of Larsen ice shelf, Antarctic Peninsula. Prominent rifts (indicated by black arrows) occur in areas of high extending flow. Rift growth is in the process of isolating a large tabular berg (white arrow). Image from http://nsidc.org (Haran et al., 2005).

Fig. 8. Schematic cryostatic and hydrostatic forces at the terminal cliff of a floating ice shelf.

Fig. 9. Episodic waterline melt-driven calving, Breiðamerkurjökull, Iceland. (A) August 7 2004. (B) July 24 2005. The terminal overhang follows the line of the crevasse trace arrowed in panel A. A second calving event occurred 2 days later along the crevasse trace arrowed in panel B.

Fig. 10. Vertical fractures and detaching lamellae at the margin of lake-calving glaciers, New Zealand. (A) Maud Glacier, March 1995. Note the waterline notch and overhanging ice cliff. (B) Godley Glacier, April 1994. The ice lamella measures c. 18 m high × 14 m wide × 1 m thick.

Fig. 11. (A) Back-tilted block at the terminus of Breiðamerkurjökull, September 9, 2004. (B) Tilted waterline notch on buoyant, partially detached tabular berg, Breiðamerkurjökull, August 5, 2005. (C) Water-filled rift at the point of detachment of the tabular berg shown in (B). (D) Buoyant terminal zone of Glaciar Nef, Patagonia, February 1998.

Fig. 12. Schematic illustration of first-order calving in response to longitudinal stretching. Surface crevasses propagate downward to a depth d in response to the velocity gradient ∂U_B / ∂x. Calving is assumed to occur when d = h (after Benn et al., in press).

Fig. 13. Idealised basal water pressure distributions in a subglacial aquifer. (A) Under purely hydrostatic conditions, the pressure head associated with the proglacial water body decays upglacier, because of the hydraulic conductivity of the aquifer. (B) Before water can be discharged through the aquifer, pressure must everywhere exceed the minimum value set by proglacial water level. (C) For water to be discharged, pressure must rise upglacier with a gradient dependent on the discharge and hydraulic conductivity. Water pressures are expressed as the equivalent piezometric surface (H_P = P_W / ρ_Ig), although it is not implied that such a surface exists within the glacier.

Fig. 14. A) Velocity gradients modelled using Eq. (22) and ice geometry and water depth representative of Columbia Glacier in 1988, for proglacial water densities of 1000 kg m^− 3 (‘freshwater’: dashed line) and 1030 kg m^− 3 (‘salt water’: solid line). B) Modelled crevasse depths. The terminus is assumed to be located where crevasse depth equals the ice surface elevation (dotted line), and the calving rate equal to the velocity at that point. For salt water conditions, the terminal ice cliff is higher, and the calving rate greater than the freshwater case. From Benn et al. (in press).

Fig. 15. Relationships between thinning, acceleration and calving retreat, resulting from effective pressure-dependent basal motion and the influence of longitudinal strain rate on dynamic thinning and first-order calving.

Fig. 16. Velocity, surface ablation, tide and precipitation, Columbia Glacier, 1984. The tidal data are inverted to highlight the close relationship between tide and velocity. From Krimmel and Vaughn (1987).

Fig. 17. Centreline velocities as a function of P_W / P_I and half-width W, calculated from Eq. (28). The example shown τ_D = 95 kPa, H = 480 m, C = 0.22 (values representative of the terminal zone of Columbia Glacier in 1988).

Fig. 18. Modelled stresses, crevasse depths and terminus position for an idealised outlet glacier of constant half-width of 30 km discharging into a widening fjord. (A) Driving stress and basal drag. Basal drag vanishes at the grounding line. (B) Prescribed ice surface elevation and modelled crevasse depths for dry and water-filled crevasses. (C) Plan view of outlet glacier geometry, showing position of the grounding line and the ice margin for the two crevasse scenarios. An ice shelf forms where surface crevasses are dry, and calving occurs at the fjord widening. Where water filled crevasses are prescribed on the lower glacier, the calving margin retreats to a grounded position.