A review of volume-area scaling of glaciers.

Volume-area power law scaling, one of a set of analytical scaling techniques based on principals of dimensional analysis, has become an increasingly important and widely used method for estimating the future response of the world's glaciers and ice caps to environmental change. Over 60 papers since 1988 have been published in the glaciological and environmental change literature containing applications of volume-area scaling, mostly for the purpose of estimating total global glacier and ice cap volume and modeling future contributions to sea level rise from glaciers and ice caps. The application of the theory is not entirely straightforward, however, and many of the recently published results contain analyses that are in conflict with the theory as originally described by Bahr et al. (1997). In this review we describe the general theory of scaling for glaciers in full three-dimensional detail without simplifications, including an improved derivation of both the volume-area scaling exponent γ and a new derivation of the multiplicative scaling parameter c. We discuss some common misconceptions of the theory, presenting examples of both appropriate and inappropriate applications. We also discuss potential future developments in power law scaling beyond its present uses, the relationship between power law scaling and other modeling approaches, and some of the advantages and limitations of scaling techniques.

End of the Little Ice Age in the Alps forced by industrial black carbon.

Glaciers in the European Alps began to retreat abruptly from their mid-19th century maximum, marking what appeared to be the end of the Little Ice Age. Alpine temperature and precipitation records suggest that glaciers should instead have continued to grow until circa 1910. Radiative forcing by increasing deposition of industrial black carbon to snow may represent the driver of the abrupt glacier retreats in the Alps that began in the mid-19th century. Ice cores indicate that black carbon concentrations increased abruptly in the mid-19th century and largely continued to increase into the 20th century, consistent with known increases in black carbon emissions from the industrialization of Western Europe. Inferred annual surface radiative forcings increased stepwise to 13-17 W⋅m(-2) between 1850 and 1880, and to 9-22 W⋅m(-2) in the early 1900s, with snowmelt season (April/May/June) forcings reaching greater than 35 W⋅m(-2) by the early 1900s. These snowmelt season radiative forcings would have resulted in additional annual snow melting of as much as 0.9 m water equivalent across the melt season. Simulations of glacier mass balances with radiative forcing-equivalent changes in atmospheric temperatures result in conservative estimates of accumulating negative mass balances of magnitude -15 m water equivalent by 1900 and -30 m water equivalent by 1930, magnitudes and timing consistent with the observed retreat. These results suggest a possible physical explanation for the abrupt retreat of glaciers in the Alps in the mid-19th century that is consistent with existing temperature and precipitation records and reconstructions.

A reconciled estimate of glacier contributions to sea level rise: 2003 to 2009.

Glaciers distinct from the Greenland and Antarctic Ice Sheets are losing large amounts of water to the world's oceans. However, estimates of their contribution to sea level rise disagree. We provide a consensus estimate by standardizing existing, and creating new, mass-budget estimates from satellite gravimetry and altimetry and from local glaciological records. In many regions, local measurements are more negative than satellite-based estimates. All regions lost mass during 2003-2009, with the largest losses from Arctic Canada, Alaska, coastal Greenland, the southern Andes, and high-mountain Asia, but there was little loss from glaciers in Antarctica. Over this period, the global mass budget was -259 ± 28 gigatons per year, equivalent to the combined loss from both ice sheets and accounting for 29 ± 13% of the observed sea level rise.

Contribution potential of glaciers to water availability in different climate regimes.

Although reliable figures are often missing, considerable detrimental changes due to shrinking glaciers are universally expected for water availability in river systems under the influence of ongoing global climate change. We estimate the contribution potential of seasonally delayed glacier melt water to total water availability in large river systems. We find that the seasonally delayed glacier contribution is largest where rivers enter seasonally arid regions and negligible in the lowlands of river basins governed by monsoon climates. By comparing monthly glacier melt contributions with population densities in different altitude bands within each river basin, we demonstrate that strong human dependence on glacier melt is not collocated with highest population densities in most basins.