Now a team from Switzerland has developed a technique for better estimating glacier volume from information about surface topography and mass balance – data that are relatively easy to obtain for a large number of glaciers. They used an inverse approach, working backwards from a "forward model" that calculates surface topography from subglacial topography and mass balance. The approach is based on the shallow-ice approximation of ice flow and removes the need for assumptions required by several other techniques, which typically employ surface-velocity data.

The researchers, from EPFL and ETH Zürich, adapted a method that reconstructs the bed topography of a steady river using the Saint-Venant Shallow Water Approximation, but used more complex geometries. Initially they assumed a steady-state surface for the glacier and solved its subglacial topography in 2D, before extending their analysis further.

"Basically, the method improves the accuracy of estimations of the glaciers' ice-thickness distributions, in the sense that up to now, only lower-order approximations were used," Laurent Michel of EPFL told environmentalresearchweb. "One can extend the method to take into account the 3D reality of the glaciers and also higher-order models describing the ice dynamics more precisely. In particular, if the ice-thickness distribution is better known, then better estimations of the glaciers' volume can be done, and hence better forecasts of their implications for sea-level rise."

According to Michel, the technique means the researchers "do not need to filter surface data where its gradient is zero" or to make "global assumptions for the basal shear stress, which some people approximate with a formula involving interpolation coefficients and the glacier's elevation range".

The team modelled the thickness of the Muragl Glacier, the Silvretta Glacier and the Rhône Glacier, all in the Swiss Alps, under both a steady-state and transient surface geometry in 2D. They also analysed Muragl Glacier in three dimensions.

"The most relevant work our contribution builds on is theoretical developments of the glaciological forward models," said Michel. "Once these models exist, we can think of ways to invert them."

Michel is currently developing a Lagrangian-based method to solve the same problem in 2D and 3D. "There may be an implementation of the Lagrangian method with a full Stokes model," he said.

The researchers reported their work in Inverse Problems.