论文标题
揭示水蒸气分布的分形性质
Uncovering the Fractal Nature of Water Vapor Distribution above the Surface of the Earth
论文作者
论文摘要
最近，分形一直是地球物理和地理空间研究的核心。我们研究了地球表面上方水蒸气分布的新兴分形特征，这是图像分辨率（像素数）和水分含量百分位数的函数。我们使用计算方法和算法计算出物理相关的数量，例如分形维数，簇数和最大簇的大小，具有不同的蒸气百分位。我们的分析揭开了数据的潜在多骨干性特征，我们使用盒子计数方法构建该特征来计算广义维度。我们研究了随着蒸气百分位数的变化，并对过渡的通用类别发表评论。我们测试了Korcak定律在系统上的适用性，并使用Kolmogorov-Smirnoff统计数据确定拟合质量。我们表明，分布的分形特征是图像分辨率的函数，并且在某些机制中与蒸气百分位数的函数近似。
Fractals have been at the heart of geophysical and geospatial studies in the recent past. We examine the emergent fractal character of water vapor distributions above the surface of the Earth as a function of both image resolution (number of pixels) and moisture content percentile. We calculate physically relevant quantities such as fractal dimension, number of clusters, and size of the largest cluster with varying vapor percentile using computational methods and algorithms. Our analysis unravels a potential multi-fractal character of the data which we construct using the box-counting method to calculate the generalized dimension. We examine the nature of the percolation that occurs as the vapor percentile is varied and comment on the universality class of the transition. We test the applicability of Korcak's law on our system and determine the quality of the fit using the Kolmogorov-Smirnoff statistic. We show that the fractal character of the distribution is exact as a function of image resolution and approximate in some regimes as a function of the vapor percentiles.
