[1] Basal drag is a fundamental control on ice stream dynamics that remains poorly understood or constrained by observations. Here, we apply control methods on ice surface velocities of Pine Island Glacier, West Antarctica to infer the spatial pattern of basal drag using a full-Stokes (FS) model of ice flow and compare the results obtained with two commonly-used simplified solutions: the MacAyeal shelfy stream model and the Blatter-Pattyn model. Over most of the model domain, the three models yield similar patterns of basal drag, yet near the glacier grounding-line, the simplified models yield high basal drag while FS yields almost no basal drag. The simplified models overestimate basal drag because they neglect bridging effects in an ice stream region of rapidly varying ice thickness. This result reinforces theoretical studies that a FS treatment of ice flow is essential near glacier grounding lines. Citation: Morlighem, M., E.

[1] The traditional method for interpolating ice thickness data from airborne radar sounding surveys onto regular grids is to employ geostatistical techniques such as kriging. While this approach provides continuous maps of ice thickness, it generates products that are not consistent with ice flow dynamics and are impractical for high resolution ice flow simulations. Here, we present a novel approach that combines sparse ice thickness data collected by airborne radar sounding profilers with high resolution swath mapping of ice velocity derived from satellite synthetic-aperture interferometry to obtain a high resolution map of ice thickness that conserves mass and minimizes the departure from observations. We apply this approach to the case of Nioghalvfjerdsfjorden (79North) Glacier, a major outlet glacier in northeast Greenland that has been relatively stable in recent decades. The results show that our mass conserving method removes the anomalies in mass flux divergence, yields interpolated data that are within about 5% of the original data, and produces thickness maps that are directly usable in high spatial-resolution, high-order ice flow models. We discuss the application of this method to the broad and detailed radar surveys of ice sheet and glacier thickness.

In this work, we propose to extend the Arlequin framework to couple particle and continuum models. Three different coupling strategies are investigated based on the L 2 norm, H 1 seminorm, and H 1 norm. The mathematical properties of the method are studied for a one-dimensional model of harmonic springs, with varying coefficients, coupled with a linear elastic bar, whose modulus is determined by simple homogenization. It is shown that the method is wellposed for the H 1 seminorm and H 1 norm coupling terms, for both the continuous and discrete formulations. In the case of L 2 coupling, it cannot be shown that the Babuška-Brezzi condition holds for the continuous formulation. Numerical examples are presented for the model problem that illustrate the approximation properties of the different coupling terms and the effect of mesh size.

[1] The ice flux divergence of a glacier is an important quantity to examine because it determines the rate of temporal change of its thickness. Here, we combine high-resolution ice surface velocity observations of Nioghalvfjerdsfjorden (79north) Glacier, a major outlet glacier in north Greenland, with a dense grid of ice thickness data collected with an airborne radar sounder in 1998, to examine its ice flux divergence. We detect large variations, up to 100 m/yr, in flux divergence on grounded ice that are incompatible with what we know of the glacier surface mass balance, basal mass balance and thinning rate. We examine the hypothesis that these anomalies are due to the three-dimensional flow of ice around and atop bumps and hollows in basal topography by comparing the flux divergence of three-dimensional numerical models with its surface equivalent. We find that three-dimensional effects have only a small contribution to the observed anomalies. On the other hand, if we degrade the spatial resolution of the data to 10 km the anomalies disappear. Further analysis shows that the source of the anomalies is not the ice velocity data but the interpolation of multiple tracks of ice thickness data onto a regular grid using a scheme (here block kriging) that does not conserve mass or ice flux. This problem is not unique to 79north Glacier but is common to all conventional ice thickness surveys of glaciers and ice sheets; and fundamentally limits the application of ice thickness grids to high-resolution numerical modeling of glacier flow. Citation:

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In this paper, we present a novel approach that allows to couple a deterministic continuum model with a stochastic continuum one. The coupling strategy is performed in the Arlequin framework, which is based on a volume coupling and a partition of the energy. A suitable functional space is chosen for the weak enforcement of the continuity between the two models. The choice of this space ensures that the mean of the stochastic solution equals the deterministic solution point-wise, and enforces appropriate boundary conditions on the stochastic dimension. The proof of the existence of the solution of the mixed problem is provided. The numerical strategy is also reviewed, in particular with a view at the Monte Carlo method. Finally, examples show the interest of the method, and possible strategies for use in adaptive modeling.

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