Extended Data Fig. 4: Schematic showing how water leakage is calculated in Eqs. (6) to (8).
From: Widespread partial-depth hydrofractures in ice sheets driven by supraglacial streams
The total leak q from the channel into the fracture is treated as the sum of many small leaks δq (Eq. (7)). Each small leak is calculated using Toricelli’s equation (Eq. (6)); these are integrated around the curved perimeter of the channel cross section from ϕ = 0 to ϕ = π (Eq. (8)). In the ’slow’ model, the fracture width wfc just below the channel is fixed at a constant wfc = wf (as shown in Fig. 2). In the ’fast’ model, wfc increases with time close to the channel because turbulent heat transfer melts the ice where water is entering the fracture (see Eq. (13)), but remains fixed at wf elsewhere. Additional symbols are the parameter C in Toricelli’s equation, water depth h(ϕ), and channel radius rc.
