Mass and Energy Balances of Glaciers and Ice Sheets
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165: Mass and Energy Balances of Glaciers and Ice Sheets J GRAHAM COGLEY Department of Geography, Trent University, Peterborough, ON, Canada Glaciers exchange energy and mass with the rest of the hydrosphere by snowfall, melting, vapor transfer, and the calving of icebergs. Melting and vapor transfer are significant in both the energy balance and the mass balance, which in consequence are intimately coupled. Glacier energy balances differ from those of other natural surfaces in having small or even negative net radiation. Emission of terrestrial radiation is limited, the surface temperature being no greater than the freezing point, but the surface albedo is always high. The limit on surface temperature, and the year-round tendency for net radiative cooling, means that sensible heat transfer is generally downward, while vapor transfer may be either upward or downward. Once conduction has raised a surface layer to the freezing point, further energy surpluses are used to melt snow or ice. In winter, the energy balance is dominated by radiative cooling. Apart from its close connection with the energy balance, the mass balance is also influenced strongly by glacier dynamics. Glaciers and the flowlines of which they are composed exhibit vertical zonation, with net accumulation at higher and net ablation (mass loss) at lower elevations. This imbalance drives, and is corrected by, the ice flow. The leading methods for the measurement of mass balance are the direct, geodetic, and kinematic methods. Direct measurement involves determining the accumulation and ablation in situ or by equivalent remote sensing, with separate treatment of calving where it occurs. Geodetic measurements require the determination of glacier thickness at two epochs; the change of thickness, approximately equal to the change in surface elevation, gives a volume balance that may be converted to a mass balance if the density of the mass gained or lost can be supplied accurately. In the direct and geodetic approaches, the ice flow is assumed to integrate to zero over any one flowline (correctly, if the entire flowline is measured). Kinematic methods are free of this restriction. They involve measurement of all of the terms in the balance and are therefore more difficult. The need for better understanding of mass balance, at socioeconomic scales from local to global, has stimulated intense study of ways to improve the measurements. Recent and impending methodological advances are coming from radar altimetry, laser altimetry, gravimetry, passive-microwave remote sensing, and interferometry using synthetic aperture radar. A subject requiring increased attention, as the measurements improve in precision and coverage, is improved quantification of the measurement errors. The best current estimates of global average mass balance are equivalent to 0.14–0.44 mm a−1 of sea-level rise, to be compared with the inferred total rate of about 1.9 mm a−1 . This figure is a composite of estimates for “small” glaciers (those other than the ice sheets), whose balance has been growing more negative since the 1960s; the Greenland Ice Sheet, which seems to have a negative balance; and the Antarctic Ice Sheet, for which the sign of the mass balance remains in doubt although its magnitude is probably within a few kg m−2 a−1 (mm a−1 water-equivalent) of zero. INTRODUCTION from that of a drainage basin or other hydrological unit, the fact that glaciers have a basal energy balance and a Glaciers exchange energy with the atmosphere overlying (typically small) internal energy balance sets them apart. them and with the earth or ocean beneath. While the surface A more obvious distinguishing feature of glaciers is that, energy balance of a glacier is not fundamentally different because they are made of frozen water which is apt to Encyclopedia of Hydrological Sciences. Edited by M G Anderson. 2005 John Wiley & Sons, Ltd. 2556 SNOW AND GLACIER HYDROLOGY melt, their energy and mass balances are very intimately ordinarily be exposed to the atmosphere, but there may coupled. Mass balance is the glaciological analog of the be a complicating mantle of rocky debris (Nakawo et al., water balance in hydrology. Most glaciers gain mass by 2000). Melting and freezing are regarded as loss and gain snowfall and lose mass by melting, although for some respectively; that is, liquid water is “outside” the column, glaciers, including the largest, the calving of icebergs is being assumed to run off or refreeze in a time shorter than an important term in the balance. the span over which we compute the mass balance (of ice). Glacier energy and mass balances are important in the The column also has internal energy and mass balances; for following unranked respects: example, changes of water phase are not restricted to the surface and the base. • Glacier meltwaters are dominant components of the water balance of semiarid regions downstream of Flowline glacierized mountain ranges (e.g. Su and Shi, 2002). Such regions include the Prairies of Canada, Central A flowline (Figure 1b) is a sequence of ice columns of Asia, and the Himalaya, and much of Andean South infinitesimal cross section arranged so that each column America. They also constitute an important resource for gains mass by flow from an up-ice neighbor and loses hydroelectric power generation, notably in Norway; a mass to a down-ice neighbor. To a good approximation, source of revenue from tourism; and hazards (Richard- flowlines may be identified by beginning at any point where son and Reynolds, 2000). either the slope changes sign – at a flow divide – or the • On the global scale, glaciers exchange mass with the ice thickness drops to zero, and following the direction ocean. As it is currently understood, the water balance of steepest ascent or descent to another such point. The of the ocean fails to add up and an accurate knowledge first column in the sequence has zero flow through one of glacier mass balance is required if we are to explain boundary. Most importantly, the integral of the mass flux the observed contemporary rise of sea level (Church divergence over the entire flowline is zero: a loss by et al., 2001; Munk, 2003). Glacier mass balance also flow from one part of the flowline must be compensated affects the salt balance of the ocean. by a gain somewhere else, which means that we can • Glaciers play a part both in bringing about climatic neglect the flow when estimating the mass balance of change and in helping us to document it. They are the flowline. highly reflective and so reduce the magnitude of net radiation at the Earth’s surface, and as their extents Glacier change so does their influence on the global energy balance and the general circulation. As independent A glacier is a collection of contiguous complete flowlines sources of information about environmental change, through snow and ice that persists on the Earth’s surface they are a valuable supplement to the weather stations for more than one year (Figure 1c). The two largest glaciers from which we derive information about temperature are called ice sheets: the Greenland Ice Sheet and the and other leading climatic variables. Antarctic Ice Sheet. An ice shelf consists of the floating • Gains and losses of glacier mass imply redistribution of parts of two or more glaciers. There are small ice shelves the mass of the Earth, altering its moments of inertia in northernmost Canada and Greenland, but otherwise ice with consequences for the evolution of such geophysical shelves are found only in Antarctica. Ice shelves differ quantities as length-of-day, true polar wander and the from sea ice, which is a few meters thick, in being tens geoid, and with implications for understanding of the to thousands of meters thick. viscosity profile of the Earth’s mantle (Peltier, 1998). Glacier Types and Glacier Zones Glaciers are at or below their freezing point Tf,whichin DEFINITION OF TERMS the absence of impurities increases from 273.16 K at the −1 A Column of Ice surface at a rate of about 0.67 K km of ice overburden. Cold or polar glaciers are those in which temperature In Figure 1(a), a column extends through ice at the Earth’s T is below Tf except possibly in a surface layer, up to surface. Ice, a soft solid, deforms readily under stress, 10–15 m thick, during summer. Temperate glaciers are so we orient the column with respect to the resulting at T = Tf throughout, except in the surface layer during flow. We assume that net exchanges of energy and mass winter. Polythermal glaciers have, in addition to the surface through the side-walls are negligible, an idealization which layer of seasonal fluctuations, a basal layer at T = Tf and is acceptable for balance studies if not for studies of an intermediate layer in which T<Tf.Coldglaciersare dynamics. The lower surface makes contact with either the also dry-based glaciers, while polythermal and temperate solid earth or water. At its upper surface, the column will glaciers are, at least locally, wet-based glaciers. These types MASS AND ENERGY BALANCES OF GLACIERS AND ICE SHEETS 2557 e Divide p e w Grounding line Terminus w p m (ice front) qin m (b) Start of flowline End of flowline qout f m p Precipitation; internal accumulation e Sublimation; condensation w Wind drifting, scouring m Meltwater runoff f Basal freezing q Ice flow (a) (c) Figure 1 (a) A column of ice, showing leading mass-balance terms. Black arrows: accumulation (gain of mass); white arrows: ablation (loss of mass); grey arrows: throughflow. (b) A flowline considered as a sequence of ice columns. This flowline happens to have a floating terminal section.