Universal Fractal Scaling Laws for Surface Water Bodies and Their Zones of Influence

Abstract

It is widely known that there are several interdependent phenomena. The zones of influence (ZoIs) of water bodies (WBs) can be considered as typical examples. Over 289000 ZoIs are computed for the corresponding WBs mapped from remotely sensed satellite data of Indian peninsular. The size of WBs ranges between the smallest size of 5.1594 m 2 to 628.1642 km 2 , and the range of the ZoIs is in between 416.2497 m 2 to 8862.3362 km 2 . The basic geometric measures were computed for all WBs and their ZoIs. These measures were employed to derive power laws that are found scale-invariant, supporting the fact that these interdependent phenomena belong to two different universality classes, and explaining the commonly shared physical mechanisms. It is also inferred that power laws derived for this very large set of WBs and their ZoIs are similar to the ones derived for a smaller data set, that is, they are indeed fractals. The study shows the importance of deriving power-law relationships for natural phenomena mapped from remotely sensed satellite data across very fine to coarse spatial, spectral, and temporal resolutions.