Quaternary Science Reviews 28 (2009) 1831–1849 Contents lists available at ScienceDirect Quaternary Science Reviews journal homepage: www.elsevier.com/locate/quascirev Modeling ice sheets from the bottom up T. Hughes* Department of Earth Sciences, Climate Change Institute, University of Maine, Bryand Global Sciences Center, Grove Street Extension, Orono, ME 04469-5790, USA article info abstract Article history: Three facts should guide ice-sheet modeling. (1) Ice height above the bed is controlled by the strength of Received 6 November 2008 ice-bed coupling, reducing ice thickness by some 90 percent when coupling vanishes. (2) Ice-bed Received in revised form coupling vanishes along ice streams that end as floating ice shelves and drain up to 90 percent of an ice 25 May 2009 sheet. (3) Because of (1) and (2), ice sheets can rapidly collapse and disintegrate, thereby removing ice Accepted 6 June 2009 sheets from Earth’s climate system and forcing abrupt climate change. The first model of ice-sheet dynamics was developed in Australia and applied to the present Antarctic Ice Sheet in 1970. It treated slow sheet flow, which prevails over some 90 percent of the ice sheet, but is the least dynamic component. The model made top-down calculations of ice velocities and temperatures, based on known surface conditions and an assumed basal geothermal heat flux. In 1972, Joseph Fletcher proposed a six- step research strategy for studying dynamic systems. The first step was identifying the most dynamic components, which for Antarctica are fast ice streams that discharge up to 90 percent of the ice. Ice-sheet models developed at the University of Maine in the 1970s were based on the Fletcher strategy and focused on ice streams, including calving dynamics when ice streams end in water. These models calculated the elevation of ice sheets based in the strength of ice-bed coupling. This was a bottom-up approach that lowered ice elevations some 90 percent when ice-bed coupling vanished. Top-down modeling is able to simulate changes in the size and shape of ice sheets through a whole glaciation cycle, provided the mass balance is treated correctly. Bottom-up modeling is able to produce accurate changes in ice elevations based on changes in ice-bed coupling, provided the force balance is treated correctly. Truly holistic ice-sheet models should synthesize top-down and bottom-up approaches by combining the mass balance with the force balance in ways that merge abrupt changes in stream flow with slow changes in sheet flow. Then discharging 90 percent of the ice by ice streams mobilizes 90 percent of the area so ice sheets can self-destruct, and thereby terminate a glaciation cycle. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction produced elliptical ice-sheet profiles on a horizontal bed. Ablation rates were added and both accumulation and ablation rates were This review primarily traces the trajectory of my glaciological allowed to vary in later refinements (see Hughes, 1998, Figure 5.10). career, which began in 1968. Consequently, those who influenced In all these treatments, gravitational ice motion was resisted by my career the most are cited prominently. My apologies to other a basal shear stress proportional to the product of ice height above prominent glaciologists. A half-century ago, glaciology was being the bed and ice surface slope. The resulting ice surface was high and converted from a descriptive branch of geology to an analytical convex, even when moderate bed topography was included. Their branch of physics. Analytical reconstructions of ice sheets began dependence on the surface mass balance made them top-down with the parabolic profile of an ice sheet having a constant basal models that produced nearly steady-state ice sheets. The ice sheets shear stress on a horizontal bed (Nye, 1951). Next, the basal shear of Antarctica and Greenland today are nearly in steady state overall, stress was allowed to vary with ice velocity determined by within the accuracy of the surface mass balance. These ice sheets a constant surface accumulation rate and whether ice moved by have high convex surfaces where slow sheet flow prevails, as creep over a frozen bed (Haefeli, 1961) or by sliding over a thawed assumed in the analytical models. The Antarctic Ice Sheet often bed (Nye, 1959), using the newly published flow law (Glen, 1955) ends as floating ice shelves because ice accumulation over virtually and sliding law (Weertman, 1957a) of ice. These treatments its entire surface allows it to advance into the sea, where iceberg calving provides the primary ablation mechanism. Weertman * Tel.: þ1 207 581 2198; fax: þ1 207 581 1203. (1957b) provided the first analytical derivation of the low and E-mail address: [email protected] essentially flat surface of a floating ice shelf. In his derivation, 0277-3791/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.quascirev.2009.06.004 1832 T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849 gravitational ice motion is resisted by a longitudinal tensile stress The top-down models for sheet flow by Budd et al. (1971) and proportional to the height of ice floating above sea level. later top-down models were incompatible with important field data from Antarctica, much of it collected by tractor-train traverses 2. Modeling ice sheets from the top down during the International Geophysical Year (IGY) in 1958 and beyond. The traverses measured ice elevations, temperatures, and Numerical ice-sheet modeling was inaugurated by William accumulation rates at the surface and ice heights above the bed Budd, Richard Jenssen, and Uwe Radok in 1971. They developed along traverse routes. The data, traverse routes, and geographical a steady-state flowline model which they applied to the Antarctic features appeared on the 1970 map, Antarctica, published by the Ice Sheet in order to derive variations of temperature, stress, and American Geographical Society. Contoured bed topographic data velocity with depth, using measured ice heights above the bed, ice showed that most of the West Antarctic Ice Sheet was grounded elevations above sea level, ice surface accumulation rates, and ice below sea level on the Antarctic continental shelf (Bentley and surface temperatures (Budd et al., 1971). From these data, their Ostenso, 1961), leading Mercer (1970) to propose that it was an model plotted ice trajectories and timelines with depth along inherently unstable ‘‘marine’’ ice sheet. Contoured surface eleva- surface flowlines, and calculated either basal ice temperatures tion data showed the East Antarctic Ice Sheet had the convex below the melting point or basal ice melting rates at the melting surface produced by steady-state models of sheet flow, but the point for specified rates of the basal geothermal heat flux. Doubling West Antarctic Ice Sheet had a concave surface. Perhaps the West the geothermal heat flux converted a ubiquitously frozen bed into Antarctic Ice Sheet was far from steady state and in fact was in an a largely thawed bed. Widespread changes from a frozen to advanced stage of gravitational collapse that produced the low a thawed bed also resulted from moderate changes in conditions at floating ice shelves surrounding it. My response to this possibility the ice surface. An outer basal freezing zone was introduced beyond appeared in four monographs, in 1972, 1973, 1974, and 1975, under the inner basal melting zone in subsequent applications of the the acronym ISCAP (Ice Streamline Cooperative Antarctic Project), model to prevent widespread ice-bed decoupling as the basal water all of which posed the question, ‘‘Is the West Antarctic Ice Sheet layer thickened (Sugden, 1977). disintegrating?’’ Was the West Antarctic Ice Sheet not only Budd and Radok were meteorologists who saw interactions of collapsing into ice shelves, but would the ice shelves then disin- the ice surface with the atmosphere as the critical boundary tegrate into icebergs, thereby removing the West Antarctic Ice condition in modeling ice sheets. Budd et al. (1971) specified Sheet from the global climate system, and flooding the world ocean surface conditions in order to determine basal conditions. Theirs with icebergs that, in melting, would cool ocean surface water and was a top-down model in which the surface mass balance combines therefore reduce the ocean-to-atmosphere heat exchange that with the force balance to offset gravitational motion with basal drag drives atmospheric circulation? Could a new glaciation cycle then that resists motion. By that constraint, their model applied only to begin? slow sheet flow. This is known as the ‘‘shallow-ice’’ approximation (Hutter, 1983). Their pioneering work set the stage for developing 3. The Fletcher memorandum gridpoint ice-sheet models that were three dimensional and time dependent. Time-dependent modeling showed that present basal Incorporated in my ISCAP bulletins was a research strategy for thermal conditions are determined primarily by past surface studying dynamic systems proposed by Joseph Fletcher in an conditions, not present conditions, even if surface changes from internal memorandum when he headed the Office of Polar past to present are only moderate. These models also simulate only Programs at the National Science Foundation (Fletcher, 1972). slow sheet flow, which prevails over some 90 percent of ice sheets, Fletcher recommended research that answered six questions past and present. In sheet flow, gravitational flow is resisted directed at how any dynamic system operates. His six questions and primarily by basal drag, as quantified by the basal shear stress. my answers for the Antarctic Ice Sheet that also apply to all ice Since past surface conditions are poorly known for present ice sheets are: sheets, and unknown for former ice sheets, top-down models cannot deliver reliable basal conditions for 90 percent of the bed 1.