1. INTRODUCTION
Thermal convection was quantified in 1916 by J. W. Strutt, Third Baron Rayleigh [1]. Thermal convection is heat transport by mass transport. It occurs in Newtonian viscous fluids heated from below, which produces warm less-dense fluid beneath cool more-dense fluid. This is gravitationally unstable, and thermal convection “stirs” the fluid to produce a state of buoyant thermal equilibrium which transfers the warm fluid to rapidly rising convection currents along side boundaries of polygonal platform cells and the cool fluid to slowly sinking convection currents within the cells between these warm boundaries. If a horizontal current of advective flow is superimposed on a fluid heated from below, the platform cells will be elongated in the direction of advective flow and become linear rolls in which convective flow spirals in the direction of advective flow [2,3]. The possibility of thermal convection in Earth’s mantle as the driving force for moving crustal tectonic plates on Earth’s surface received great attention during the mid-century revolution in Earth sciences that became known as plate tectonics. Of those treatments, the one by Johannes Weertman [4] was of particular interest in assessing the possibility of thermal convection in the Antarctic Ice Sheet [5].
If thermal convection also occurs in polycrystalline solids, such as Earth’s mantle and continental ice sheets, the strong crystal anisotropy and temperature dependence of creep in these solids would make rising currents much narrower and faster than sinking currents in cells and rolls, compared to these currents in Newtonian fluids. For possible thermal convection in large ice sheets, past, present, and future, which are heated from below by geothermal and frictional heat, platform cells would be most likely along internal ice divides where advective flow is minimal and these cells would become rolls as advective flow increases downslope from high interior ice divides to low ice margins, usually converging on ice streams [5]. Ice streams are fast currents of ice that develop near ice-sheet margins and discharge most of the ice, much as large rivers discharge most precipitation over continents. Ice streams and rivers are supplied by numerous tributaries that drain vast interior areas. Figure 1 shows these tributaries supplying large ice streams that drain the Antarctic Ice Sheet today [6]. Are these tributaries the surface expression of underlying thermal convection rolls? That is the question addressed here. Answers to this question are also proposed.
The possibility of thermal convection in the Antarctic Ice Sheet gained attention in the 1970s after ice temperatures and densities were obtained in 1968 from a corehole drilled 2164 m to bedrock at Byrd Station (80˚S, 120˚W) in the center of West Antarctica [7]. The corehole data revealed a density inversion about halfway down that separated cold upper ice from warmer lower ice. These data allowed a Rayleigh number to be calculated, following the theory for initiating thermal convection in Newtonian fluids heated from below, and delivered a Rayleigh number Ra just above the critical value Ra* that allows thermal convection [8]. For thicker ice, common in Antarctica, the Rayleigh number would be significantly above critical. The Rayleigh number is a dimensionless measure of the rate of heat transported by mass transport of hot atoms (thermal convection) compared to the rate of heat transported by the thermal vibrational energy of atoms remaining in place (thermal conduction). Convection begins when this ratio attains a critical threshold that overcomes resistance to mass transport.
A section, Old Data, Old Ideas, reviews attempts over the past four decades to find conclusive evidence for thermal convection in the Antarctic and Greenland Ice Sheets. A section, New Data, New Ideas, presents a hypothesis that ice-stream tributaries are the surface expression of convection rolls in the Antarctic Ice Sheet, and new data showing these tributaries are ubiquitous and extend from ice divides to major ice streams. A section, Theory, examines the physical basis of the Rayleigh criterion for initiating thermal convection in ice sheets as transient creep that may become steady-state creep with a gravitational driving stress comparable to that for slow sheet flow and fast shelf flow in Antarctica. A section, Conclusions, discusses the implications of this kind of thermal convection in terms of ice-sheet stability, climate records stored in ice sheets, and thermal convection in Earth’s mantle.
2. OLD DATA, OLD IDEAS
Evidence for and against thermal convection in the Antarctic Ice Sheet was presented in the 1970s and 1980s. Many years ago, I asked Barclay Kamb, our most innovative field glaciologist (recently deceased), if he could design a field experiment that would unambiguously detect convective flow, if it existed. After some time passed he told me he couldn’t think of one. It has been a challenge to find convincing evidence, even though the theoretical case for convection seems compelling to me.
When radar sounding was first used in both East and West Antarctica, it produced columnar reflections suggesting rising convection plumes [9], but they were soon shown to be specular echoes unrelated to ice flow [10, 11]. In 1981, W. S. B. Paterson maintained that the most convincing evidence against thermal convection was undisturbed stratigraphic radio-echo reflecting horizons extending for hundreds of kilometers all over the Antarctic Ice Sheet [12]. However his figure to “prove” his point showed that an echo-free zone was equally widespread in ice below the probable density inversion, where thermal convection would scramble the ice and erase these horizons [13].
Local radar records from East Antarctica in 1982 showed internal reflecting horizons at two sites, one along advecting ice flow and one transverse to this flow [14]. Both had a lower echo-free zone. Higher ice had horizontal stratigraphy in the longitudinal record, but this ice was bent into a series of arches in the transverse record. Both records had rugged beds that didn’t conform with the radar records. These records might be produced by thermal convection rolls, with no distortion of radar reflections along rolls, but arching these reflections across rolls [13], see also Figure 4 and discussion in Ice Sheets [15]. Radar records generally did not show this arching pattern where conditions for thermal convection seemed to be equally favorable. Advances in radar-sounding technology now deliver reflecting horizons in the “echo-free zone” but these tend to be discontinuous and warped [16], conditions thermal convection might produce.
Theoretically, it was necessary to show how the Rayleigh criterion should be modified to allow thermal convection in crystalline solids such as ice, and not just in Newtonian fluids [1,17,18]. The first and only comprehensive theoretical paper promoting thermal convection in the Antarctic Ice Sheet [5] employed the Weertman [4] analysis of thermal convection in Earth’s upper mantle (the asthenosphere) using a two-dimensional “block model” of thermal convection that would apply to convection rolls in transverse cross-section. Polycrystalline solids with strong crystal anisotropy, such as mantle minerals and glacier ice, are suited to the block model because shear boundaries become sharply defined. The Weertman theory of thermal convection in polycrystalline solids produces convection rolls having a roll diameter about twice the roll depth [4]. Applying this to the Antarctic Ice Sheet, rolls would be 4 to 6 km wide for ice 2 to 3 km thick. Ice-stream tributaries typically have these widths and depths.
Because ice deforms near the plastic end of the viscoplastic creep spectrum, thermal convection might exist as ascending dikes in narrow shear bands that intrude horizontal ice strata as multiple narrow sills. A dyke-sill version of the block model was used to “explain” the spikiness of oxygen-isotope stratigraphy found below the density inversion in coreholes to bedrock for the Greenland and Antarctic ice sheets [19]. Spikes would be sills having a different isotope signature. Today this spikiness is attributed to Late Pleistocene environmental effects that may or may not be linked to conventional ice-sheet dynamics [20].
3. NEW DATA, NEW IDEAS
In 2009, a new perspective on how convective and advective flow could be linked [21] followed the 1976 suggestion that tributaries supplying major Antarctic ice streams are the surface expression of underlying convection rolls [5]. Figure 1 illustrates this new perspective. It is a most striking display of ice-stream tributaries on a full map of Antarctic ice flow using NASA technology to piece together satellite-sensing data from the European Space Agency (ESA), the Japanese Space Agency (JSA), and the Canadian Space Agency (CSA). Figure 1 was produced in the Earth System Science Department at the University of California, Irvine, and the Jet Propulsion Laboratory of the California Institute of Technology [6].
Figure 1. A full map of Antarctic ice flow showing tributaries supplying major ice streams. This map was compiled by NASA-funded research at the Jet Propulsion Laboratory of the California Institute of Technology and the Earth System Science Department at the University of California at Irvine, using data from Earth-orbiting satellites provided by the Japanese, European, and Canadian Space Agencies. Ice velocities increase from orange near interior ice divides to green in ice tributaries to blue in ice streams to red on ice shelves. A video showing motion of the tributaries is available on the NASA News website. Here we propose that ice tributaries are underlain by and driven by thermal-convection rolls aligned with surface ice flow. From NASA News, http://www.jpl.nasa.gov/ news/news.cfm?release=2011-256&cid=release.
Dozens of scientists from many countries contributed to this enterprise. If the new perspective is correct, Figure 1 shows that thermal convection is widespread in the Antarctic Ice Sheet.
Figure 1 shows that fast ice-stream tributaries are about 5 km wide and are separated by slower-moving ice that narrows from about 30 km in width near ice divides to zero width as tributaries pack together and enter major ice streams. These tributaries begin near interior ice divides and fill the ice drainage basins supplying major Antarctic ice streams. If ice-stream tributaries are the surface expression of underlying thermal convection rolls, Figure 1 is a map of thermal convection rolls within the Antarctic Ice Sheet. Thermal convection then exists throughout the ice sheet, being strongest at depth but also directing surface advective flow. Modeling advective flow superimposed on convective flow would require using all six deviator stresses, with all six stresses linked to strain rates [22].