The surface restitution method we present reconstructs the evolution of a glacier surface between two time-separated surface topographies using seasonal surface mass balance (SMB) data. A conservative and systematic error analysis is included, based on the availability of surface elevation measurements within the period. The method is applied from 2001 to 2013 at Hurd Glacier (a 4 km2 glacier), where we have sufficient SMB and elevation data. We estimate surface elevation changes in two steps: (1) elevation change due to SMB and (2) elevation change due to glacier dynamics. Four different models of the method are compared depending on whether or not accumulation is memorised at each time step and whether they employ balance profiles or SMB maps. Models are validated by comparing a set of surface measurements retrieved in 2007 with the corresponding restituted elevations. Although surface elevation change between 2001 and 2007 was larger than 10 m, more than 80% of the points restituted by the four models showed errors below ±1 m compared to only 33% when predicted by a linear interpolator. As error estimates between models differ by 0.10 m, we recommend the simplest model, which does not memorise accumulation and interpolates SMB by elevation profiles.

We determine the steady-state structures that result from liquid-liquid demixing in afree surface film of binary liquid on a solid substrate. The considered model correspondsto the static limit of the diffuse interface theory describing the phase separationprocess for a binary liquid (model-H), when supplemented by boundary conditions at thefree surface and taking the influence of the solid substrate into account. The resultingvariational problem is numerically solved employing a Finite Element Method on an adaptivegrid. The developed numerical scheme allows us to obtain the coupled steady-state filmthickness profile and the concentration profile inside the film. As an example wedetermine steady state profiles for a reflection-symmetric two-dimensional droplet forvarious surface tensions of the film and various preferential attraction strength of onecomponent to the substrate. We discuss the relation of the results of the present diffuseinterface theory to the sharp interface limit and determine the effective interfacetension of the diffuse interface by several means.