Flow-law hypotheses for ice-sheet modeling

Abstract

ABSTRACT. Ice-flow modeling requires a flow law relating strain rates to stresses in situ, but a flow law cannot be measured directly in ice sheets. Microscopic processes such as dislocation glide and boundary diffusion control both the flow law for ice and the development of physical properties such as grain-size and c-axis fabric. These microscopic processes can be inferred from observations of the physical properties, and the flow law can then be estimated from the microscopic processes.A review of available literature shows that this approach can be imperfectly successful. Interior regions of large ice sheets probably have depth-varying flow-law "constants", with the stress exponent, n, for power-law creep less than 3 in upper regions and equal to 3 only in deep ice; n probably equals 3 through most of the thickness of ice shelves and ice streams.

Ice Microstructure and Fabric of Guliya Ice Cap in Tibetan Plateau, and Comparisons with Vostok3G-1, EPICA DML, and North GRIP

“…We expect that the NGG can take place along the whole Guliya core as the recrystallization is the same at all depths of the EPICA DML core [5]. This is different from the classical tripartite paradigm of the polar ice [8,15,[42][43][44][45][46] which includes the NGG, the polygonization/rotation recrystallization (RRX), and the migration recrystallization (SIBM) from the top to the bottom down each core.…”

“…Within 10-101 m depth of the Guliya core, which possibly reflects periods of climatic warming and cooling (the grain diameter are evidently large at 44.0-51.0 m and 81.0-91.0 m, and distinctly small at 101.0 m in Figure 2) is consistent with the analysis of Lipenkov et al [23] for the Vostok3G-1 core and Faria et al [41] for the EPICA DML core, respectively. However, that the grain size of the Ice Age is significantly smaller than that of Holocene ice [8,27,30] has not been identified by the measurement of the Guliya ice core [22]. This can be explained by grains growing with age reaching a limited size where polygonization counteracts grain growth for the Holocene part of the EPICA DML core [20] and, by that, the grain growth of the North GRIP core for the last~2 ka is seen to be linear with time, while the grains older than 2 ka merely approach a constant area (Figure 2), which is probably a result of polygonization [17].…”

“…The grain growth is driven primarily by two factors: the curvature of energetic grain boundaries and the differences in stored strain energy among grains. The average grain size decreases or stops increasing by two processes: polygonization, where the existing grains are subdivided [8,15], and recrystallization, in which new grains are created [8]. The mean grain size of polycrystalline ice increases over time by grain growth in the absence of mechanisms to form new grains [1], i.e., the Normal Grain Growth (NGG) depends upon the migration which is driven by curvature of the boundaries in slowly deforming ice.…”

“…However, it has been reported in Antarctica, at the Vostok3G-1, where vertical girdles appear through to the bottom of the borehole from the depth of 454 m [23], at EPICA DLM at 450-1700 m [5,20], and in Greenland, at the North GRIP, at 805-2500 m [17,27] (Figure 3). Furthermore, Fujita et al [47], Lipenkov et al [23], and Alley [7,8] perform computer simulation and explanation of vertical girdle formation. It is regarded as resulting from gradual rotation of grain by basal glide under uniaxial longitudinal tension, without recrystallization, at low temperature and strain rates.…”

“…Some micro-processes, such as lattice dislocation, intra-grain sliding, and diffusion creep with respect to the temperature of ice since its formation can be used to deduce inversely the paleo-air-temperature, ice-flow control laws, c-axis fabrics, and grain sizes. For this reason, constructing the relationship between the evolution of microstructure and fabric and climate change [6][7][8][9][10][11][12][13] is meaningful work, even though it is challenging and complex. Ice microstructure challenging and complex.…”