The thinning rate at the grounding line was computed by evaluating an equation of continuity during the model-time intervals required for each increment of grounding-line retreat. The accumulation rate, the rate of advection of thicker ice from up-glacier, and the vertical strain-rate caused by the tendency of the ice shelf to spread were taken into account. The rate of grounding-line retreat was then found by invoking a requirement that the ice remain in hydrostatic equilibrium (Reference Thomas and BentleyThomas and Bentley 1978). The change in the ice-stream thickness profile was computed by solving an equation of continuity along the flow band, during the time intervals required for each increment of grounding-line retreat.

The ice stream was assumed to move by basal sliding, and sliding was assumed to be governed by a relationship of the kind determined experimentally by Reference Budd, Keage and BlundyBudd and others (1979). The bed-roughness factor in this sliding relation was replaced, however, by an empirical sliding function with values determined by relating the base stress, thickness, and balancevelocity profiles along the flow band. The basal sliding relation was thus scaled to the ice stream, using an assumption that it is, at present, in a state of mass balance.

Elastic up lift of the Earth caused by Holocene thinning of the flow band was found by using the elastic Green’s functions computed by Reference FarrellFarrell (1972). The viscous component of uplift was found by using Green’s functions computed for an Earth model consisting of a three-dimensional viscous half-space (upper mantle) overlain by an elastic plate (lithosphere)(Reference CathlesCathles 1975: 267–272), Time-dependent isostatic up lift at all points along the central flow line was found by con-volving a load function equal to the change in the thickness profile with the elastic and viscous Green’s functions, periodically during grounding-line retreat.

The following initial conditions and assumptions were used. (1). The ice stream was initially grounded to the edge of the continental shelf in the Ross Sea, as reconstructed by Reference Hughes, Denton, Andersen, Schilling, Fastook, Lingle, Denton and HughesHughes and others (1981), and in dynamic equilibrium such that the retreat rate was zero. (2). The Earth was initially depressed, and in isostatic equilibrium. (3). An ice shelf formed seaward of the retreating grounding line. (4). The shear stress between the ice shelf and its sides was 0.65 bar. (5). The Ross Ice Shelf calving front retreated so that the ice-shelf front attained its present position by 3 ka BP. (6). Eustatic sea level rose by 130 m during the Holocene, according to a curve similar to that of Reference Milliman and EmeryMilliman and Emery (1968).

Elastic and viscous uplift of the Earth, caused by thinning of the flow band, was found to delay grounding-line retreat relative to computed retreat when the ice stream was assumed to be resting on a rigid bed. Grounding-line retreat was found to begin very slowly, at 15 ka BP, because of rising eustatic sea-level. Retreat accelerated after about 30 km, at 13 ka BP, because of increasing water depth and a sea-bed sloping down toward the ice-sheet interior. After 8 k model years, i.e. by 8 ka BP, the feedback effects of isostatic uplift caused grounding-line retreat to be delayed by about 1 ka, relative to computed retreat on a rigid Earth. The elastic and viscous Earth response exerted a moderating influence on the computed retreat rate, because uplift at the grounding line partially counteracted the effect of increasing water depth.

Grounding-line retreat slowed, and gradually stopped, near the present position of the grounding-line of ice stream E. Isostatic uplift caused the total retreat distance to be reduced by 80 km, relative to retreat computed on a rigid Earth model. A re-advance of 20 km of the model grounding line occurred between 3 ka BP and the present, because continuing viscous uplift caused sea depth to decrease.

Resistance from the Ross Ice Shelf was found to be of primary importance in bringing grounding-line retreat to a stop in the Ross embayment, as determined earlier by Reference Thomas and BentleyThomas and Bentley (1978). In addition, the timing of retreat of the ice-shelf calving front was found to exert a major influence on the timing of grounding-line retreat. Reliable methods for predicting the rate at which an ice-shelf calving front should retreat or advance due to iceberg calving do not exist, so the ice-shelf retreat history is a large source of uncertainty in the computed timing of grounding-line retreat. Alternative retreat histories for the ice-shelf calving front were investigated, subject to control provided by a date from the basal portion of the Holocene sediment layer on the bottom of the Ross Sea (Reference Kellogg, Osterman and StuiverKellogg and others 1979). Within the context of a given ice-shelf retreat history, the feedback effects of isostatic up lift caused a reduction of the grounding-line retreat rate, a reduction of the total computed retreat distance, and a readvance of the grounding line after the eustatic sea-level stopped rising.