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 iO of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how iO varies along these flow bands where surface and bed topography are known: iO = 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 (iO= 0) has gone in collapsing into a low flat ice shelf (iO= 1). Here iO captures ice bed coupling under an ice stream and h_O captures ice bed coupling beyond ice streams.
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