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Abstract
Glaciers are continuously monitored to detect their spatial extension and time evolution since they are the best witnesses of climate changes. There is a particular interest for Italian glaciers in the Alps as there is evidence that they are melting at a faster rate than those located in other regions of the globe. The determination of the perimeters of glaciers represents an effective method to evaluate the area covered by them. The availability of data for the perimeters encompassing several years suggests the opportunity of correlating the morphological variations in time with the properties of their shrinkage. In this work, we investigate the multifractal properties of the perimeters of the Lombardy glaciers in the Italian Alps. We characterize the area and perimeter distributions of the population of glaciers and we show that the distribution of perimeters exhibits a marked peak, not present in the distribution of areas. We analyze the area-perimeter relation, which is characterized by a power-law behavior that indicates a fractal structure of the perimeters with fractal dimension 1.2, independently from the size of the glaciers. We investigate the multifractal spectra of perimeters and we show that their features are strongly correlated with the area of the glaciers. Finally, we study the time evolution of the area and perimeter of glaciers and we detect the existence of a large class of glaciers whose perimeters increase while their areas decrease. We show that this behavior has a well definite counterpart in their multifractal spectra.
Highlights
The study of glaciers and the monitoring of their evolution in time is a problem of great interest, as it is directly related to the effects of global warming [1,2,3,4], the melting rates are not trivially explained by climate variability
Independently from their size, glaciers are well described as fractals with an average fractal dimension 1.2, as evidenced by the power-law area-perimeter relation
The investigation of the multifractal spectra of perimeters evidenced the existence of a correlation between multifractal properties and glaciers’ size
Summary
The study of glaciers and the monitoring of their evolution in time is a problem of great interest, as it is directly related to the effects of global warming [1,2,3,4], the melting rates are not trivially explained by climate variability. The economy of the Hindu-Kush–Karakoram–Himalaya region relies upon agriculture, and likely more than 50% of the water in the Indus river originating from the Karakoram comes from snow and glacier melt [7]. For a period of 18 days in summer 2011, Senese et al [8] quantified a total water volume of 1.54 km derived from ice melting, corresponding to 11% of the reservoir capacity of the Tarbela Dam, a very large dam on the Indus River that plays a key role for irrigation, flood control and the generation of hydroelectric power for Pakistan. On Italian Alps, and especially in the province of Sondrio in the Lombardy region where twentyseven hydropower dams are located, about one-half of the total water for hydropower plants is provided by snowfall and ice melt [9]. Observations of glacier coverage and evolution are essential to understand the role of the cryosphere in influencing the regional hydrology and water resources in these regions
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