Mass and Energy Balances of Glaciers and Ice Sheets

Abstract

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,...

Evidence for the accelerations of sea level on multi‐decade and century timescales

“…The 1920-1930 inflexion was followed in the 1940s by a high rate of global sea-level rise coinciding with a period of enhanced glacier melt (e.g. see series C05a of Cogley, 2005in Kaser et al, 2006. CW06 argued that periods of rapid surface warming tended to be followed by increased thermal expansion and high rates of global sea-level rise.…”

Extrapolating glacier mass balance to the mountain-range scale: the European Alps 1900–2100

“…Cogley, 2005;Dyurgerov and Meier, 2005;Kaser et al, 2006, partly including area-weighting schemes). The arithmetic average of mean specific mass balance of surveyed glaciers is applied to all unmeasured glaciers in a study region.…”

“…Kaser et al, 2006). The methodology suggested by Cogley (2005) applies a spatial interpolation algorithm that fits two-dimensional polynomials to the single-glacier observations. Arendt et al (2006) compare four different approaches for the regionalization of glacier mass change in the Chugach Published by Copernicus Publications on behalf of the European Geosciences Union.…”

Mass balance of glaciers and ice caps: Consensus estimates for 1961–2004

“…[6] Uncertainty of directly obtained annual surface mass balance of a single glacier is typically ±200 kg m À2 a À1 due to measurement and analysis errors [Cogley, 2005]. The main source of uncertainty is the natural horizontal variability of point mass balance, which is assumed to depend only on elevation.…”

“…Specific mass balance (left axis) is converted to total balance and to sea-level equivalent (right axis) as described in Table 1. C05a: an arithmetic mean over all annual measurements within each pentade [Cogley, 2005]; the grey confidence envelope is twice the standard error of the C05a data, and the number of measurements is given at the top of the graph. C05i, DM05, O04: spatially-corrected series obtained as described in the text.…”