We show that every knot is one crossing change away from a knot of arbitrarily high bridge number and arbitrarily high bridge distance.
In regions where ice sheets are increasing in mass, there is a 50-200 m layer of old snow called firn which does not melt in the summer months. The density of firn tracks the transformation of snow into glacial ice at approximately 917 kg m^-3. The p
rocess of firn densification is important in at least two ways: 1) it can be a dominant component in the observed rate of change of the surface elevation, and 2) storage of liquid water in the lower density firn layer is now considered a critical component in the mass balance of ice sheets. If the rate of change of surface elevation can be equated with the rate of change in the mass of the ice sheet, we would have an excellent means of monitoring ice sheet mass balance. However, knowledge of firn densification rates is needed to make the inference of mass rate of change from volume rate of change. Several firn models have been created for areas without melt. We have reformulated these models with the finite-element software package FEniCS and integrated them with an enthalpy-formulation. This integration allows us to account for the melting and subsequent re-freezing of firn layers into ice lenses.
