Abstract
AbstractA volume-area scaling relation is commonly used to estimate glacier volume or its future changes on a global scale. The presence of an insulating supraglacial debris cover alters the mass-balance profile of a glacier, potentially modifying the scaling relation. Here, the nature of scaling relations for extensively debris-covered glaciers is investigated. Theoretical arguments suggest that the volume-area scaling exponent for these glaciers is ~7% smaller than that for clean glaciers. This is consistent with the results from flowline-model simulations of idealised glaciers, and the available data from the Himalaya. The best-fit scale factor for debris-covered Himalayan glaciers is ~60% larger compared to that for the clean ones, implying a significantly larger stored ice volume in a debris-covered glacier compared to a clean one having the same area. These results may help improve scaling-based estimates of glacier volume and future glacier changes in regions where debris-covered glaciers are abundant.
Highlights
A volume-area scaling relation (Bahr and others, 1997, 2015) has been used extensively to estimate the total volume of glaciers on a regional to global scale (e.g. Grinsted, 2013), or to develop zero-dimensional models of glacier evolution (e.g. Radić and others, 2007)
I discuss the implications of the differences between the scaling relations for debris-covered and clean glaciers
To summarise the results from the above analysis of scaling relations for debris-covered glaciers: (1) The characteristic ablation rate on idealised debris-covered glaciers scale with glaciers length with the exponent md ≈ 1.5. md is smaller than the corresponding clean-glacier exponent m = 2
Summary
A volume-area scaling relation (Bahr and others, 1997, 2015) has been used extensively to estimate the total volume of glaciers on a regional to global scale (e.g. Grinsted, 2013), or to develop zero-dimensional models of glacier evolution (e.g. Radić and others, 2007). Grinsted, 2013), or to develop zero-dimensional models of glacier evolution (e.g. Radić and others, 2007). These scaling-based models are often used for numerically-efficient representation of glacier dynamics within hydrological (e.g. Zhang and others, 2015) or climate models (e.g. Kumar and others, 2019). Relates the volume of a glacier V to its area A via a dimensionless exponent γ and a scale factor c (Bahr and others, 1997, 2015). A single best-fit c, along with a fixed γ, provides a reasonable statistical description of a set of glaciers (Bahr and others, 2015). The scaling relation is interpreted in this statistical sense where all the glaciers in a given set are described with the same values of the parameters c and γ
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