In two recent papers the validity of the Shallow Ice Approximation (SIA) and its higher order extension, the Second-Order SIA (SOSIA), is analyzed. In Ahlkrona et al. (2013a) , the full Stokes equations are solved with the ice sheet/ice flow model Elmer/Ice for different aspect ratios (reflecting the shallowness of an ice sheet). By this approach it is possible to determine how the stresses, velocities and pressure depend on the aspect ratio. These dependencies, or scaling relations, are important to know correctly in order to make approximations such as the SIA. It is found that there is a thick boundary layer at the ice surface, altering the scaling relations in a way which is not considered in the classical derivation of the SIA and the SOSIA. These numerical results are consistent with existing boundary layer theory for ice sheets. In Ahlkrona et al. (2013b), we investigate, both by analysis and by numerical simulations using the ice sheet/ice flow model Elmer/Ice, how this boundary layer influences the accuracy of the SIA and SOSIA. We find that due to the boundary layer, the order of accuracy of the SIA is lower than usually assumed, and the SOSIA is in many cases not a significant improvement to the SIA and is also dependent on an ad-hoc auxiliary parameter introduced to evade singularities in the boundary layer.
Ahlkrona, J., N. Kirchner, and P. Lötstedt, 2013a. A Numerical Study of Scaling Relations for Non-Newtonian Thin-film Flows with Applications in Ice Sheet Modelling, Quarterly Journal Of Mechanics And Applied Mathematics, 66(4), 417-435, doi:10.1093/qjmam/hbt009. [link to paper]
Ahlkrona, J., N. Kirchner, and P. Lötstedt, 2013b. Accuracy of the zeroth- and second-order shallow-ice approximation – numerical and theoretical results, Geosci. Model Dev., 6, 2135-2152, doi:10.5194/gmd-6-2135-2013. [link to paper]
A short summary of this very productive year:
- more than 10 papers using the ice sheet/ice flow model Elmer/Ice were published from a much larger community than ever, a community paper summarizing the previous developments was published in GMD,
- 9 papers including results from the ice sheet/ice flow model Elmer/Ice were cited by the 5th IPCC report,
- 3 beginner courses (Univ. of Washington, USA, Univ. of Alberta, Canada and LGGE, France) and a first advanced course (CSC, Finland) were organized,
- the fist Elmer/Ice users meeting took place during EGU 2013.
Thanks all for contributing and making Elmer/Ice one of the most alive ice-sheet/ice flow model around the world! And thanks for the CSC for its continuous support in developing Elmer!
- the second Elmer/Ice users meeting will take place during EGU 2014 (Tuesday 29 May, 12:15-15:00, Room Y3)
- the examples on the svn will be soon replaced by a series of tests that can be launched automatically to verify a new installation or new developments.
- and certainly many more news to come later!
Merry Christmas and Happy New Year 2014!
The flow of glaciers and ice-streams is strongly influenced by the presence of water at the interface between ice and bedrock. In this paper, a hydrological model evaluating the subglacial water pressure is developed with the final aim of estimating the sliding velocities of glaciers. The global model fully couples the subglacial hydrology and the ice dynamics through a water-dependent friction law. The hydrological part of the model follows a double continuum approach which relies on the use of porous layers to compute water heads in inefficient and efficient drainage systems. This method has the advantage of a relatively low computational cost that would allow its application to large ice bodies such as Greenland or Antarctica ice-streams. The hydrological model has been implemented in the finite element code Elmer/Ice, which simultaneously computes the ice flow. Herein, we present an application to the Haut Glacier d'Arolla for which we have a large number of observations, making it well suited to the purpose of validating both the hydrology and ice flow model components. The selection of hydrological, under-determined parameters from a wide range of values is guided by comparison of the model results with available glacier observations. Once this selection has been performed, the coupling between subglacial hydrology and ice dynamics is undertaken throughout a melt season. Results indicate that this new modelling approach for subglacial hydrology is able to reproduce the broad temporal and spatial patterns of the observed subglacial hydrological system. Furthermore, the coupling with the ice dynamics shows good agreement with the observed spring speed-up.
Reference: de Fleurian, B., O. Gagliardini, T. Zwinger, G. Durand, E. Le Meur, D. Mair, and P. Råback, 2013. A double continuum hydrological model for glacier applications, The Cryosphere, 8, 137-153, doi:10.5194/tc-8-137-2014. [link to paper]