Multifractal analysis of glaciers in the Lombardy region of the Italian Alps

Abstract

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.