Extended Data Fig. 7: Theoretical estimates of fracture widths.
From: Widespread partial-depth hydrofractures in ice sheets driven by supraglacial streams
(a) Fracture width profiles calculated following Krawczynski et al.32 (Eq. (10)) for partially-filled fractures that have propagated to zd = 800 m. This shows how predicted fracture widths are very sensitive to water level za; it also shows the development of the constriction in the upper part of the fracture, once water level starts to drop below the surface (za/zd just above zero), which prevents us applying their model to partially-filled fractures in our study. Qualitatively similar profiles are found for other reasonable values of zd and \(\sigma {{\prime} }_{x}\). (b) Estimates of fracture widths at the surface, for completely water-filled fractures, again following Krawczynski et al.32 (Eq. (10); blue lines). For comparison, the black line represents the observed ~ 2 cm-wide fractures considered in this study (grey shaded range 1 to 3 cm). Calculations used plausible tensile far-field deviatoric stresses of 50, 100 and 200 kPa (dashes, solid, dotted lines, respectively). Although such wide surface fractures are observed following lake drainage events1,2 they are well beyond the range of widths that we have observed to be associated with supraglacial stream capture.
