Rock debris falling onto a glacier from valley walls, or plucked from its bed, is carried downstream embedded in the ice — the "conveyor belt" model of debris transport (Boulton, 1978). Surface ice speed follows a simplified Glen's-flow-law profile along the flowline fraction s (0 = head, 1 = terminus):
v(s) = v_max · sin(π s)
h_ice(s) = h_max · √(1 − s)
Velocity vanishes at the divide (no driving stress) and again near the snout (the ice has thinned toward zero); it peaks near the middle of the glacier, roughly where the equilibrium-line altitude sits. Debris advects at this local ice speed until it reaches the ablation-dominated margin, where melt-out drops it as till — unsorted, unstratified sediment (a diamicton, unlike sorted glaciofluvial outwash).
The terminus position obeys the climate mass balance: a positive balance advances the margin (bulldozing/burying till already at the front), a negative balance retreats it (exposing ground moraine as the ice melts back past debris it once carried). When the balance sits near zero for a while — a stillstand — melt-out debris keeps arriving at nearly the same spot and stacks into a terminal moraine ridge; a sequence of brief stillstands during an overall retreat leaves a staircase of recessional moraines further up-valley.
- Ice surface speed — scales v_max; faster ice delivers debris to the margin sooner.
- Debris supply rate — how often new rock debris enters the ice from the valley walls/bed.
- Climate mass balance — negative retreats the terminus, positive advances it; hold it near zero to grow a sharp terminal moraine.