Vijay K. Gupta

TL;DR: In this paper, a general class of continuous multiplicative processes is constructed to provide a theoretical framework for these observations, namely, the log-log linearity of moments with spatial scale and the concavity of corresponding slopes.

TL;DR: In this paper, the authors considered the random cascade theory for spatial rainfall and provided empirical evidence for a random cascading theory of rainfall, and the way of using data for making estimates of parameters and for making statistical inference within this theoretical framework.

TL;DR: In this paper, a kinetic theoretic framework for obtaining an explicit mathematical representation for the instantaneous unit hydrograph (iuh) at the basin outlet has been developed which lead to explicit formulae for the iuh, which are formally analogous to the solutions that would result if a basin is represented in terms of linear reservoirs and channels, respectively, in series and in parallel.

TL;DR: Recent progress and future prospects for understanding the mechanisms that generate power laws are described, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science are described.

TL;DR: In this paper, a theory of space-time rainfall, applicable to fields advecting without deformation of the coordinates, is presented and tested, where spatial rainfall fields are constructed from discrete multiplicative cascades of independent and identically distributed (iid) random variables called generators.