A 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.

中文翻译：

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碎片覆盖冰川的体积面积缩放

体积-面积比例关系通常用于估计冰川体积或其在全球范围内的未来变化。绝缘的冰上碎屑覆盖层的存在改变了冰川的质量平衡分布，可能会改变比例关系。在这里，研究了广泛覆盖的冰川的尺度关系的性质。理论论证表明，这些冰川的体积-面积比例指数比干净冰川的小约 7%。这与理想化冰川的流线模型模拟结果以及喜马拉雅山的可用数据一致。与干净的冰川相比，被碎片覆盖的喜马拉雅冰川的最佳比例因子大约大 60%，这意味着与具有相同面积的干净冰川相比，被碎片覆盖的冰川中储存的冰量要大得多。这些结果可能有助于改进对冰川体积和未来冰川变化的基于比例的估计，这些地区的冰川碎片覆盖丰富。