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.

由于冰川是气候变化的最佳见证，因此将对其进行连续监测以检测其空间扩展和时间演变。阿尔卑斯山的意大利冰川特别受关注，因为有证据表明它们的融化速度比全球其他地区的融化速度快。确定冰川的周长是评估冰川覆盖面积的有效方法。周界数据的可用性涵盖了数年，这提示了将时间上的形态变化与其收缩特性相关联的机会。在这项工作中，我们研究了意大利阿尔卑斯山伦巴第冰川外围的多重分形特性。我们表征了冰川种群的面积和周长分布，并且我们表明周长分布显示出明显的峰值，而在面积分布中不存在。我们分析了面积与周长的关系，该关系的特征是幂律行为，该行为表明分形维数为1.2的周长的分形结构与冰川的大小无关。我们研究了周界的多重分形谱，我们发现它们的特征与冰川面积密切相关。最后，我们研究了冰川面积和周长的时间演变，并发现了一大类冰川的存在，它们的周长增大而面积减小。我们表明，这种行为在其多重分形光谱中具有明确的对应关系。