A new approach to hydrological scaling

Many earth and environmental random fields and processes exhibit linear or nonlinear power-law scaling in a midrange of space and time separation distances called lags, breakdown in power-law scaling at small and large lags, recovery of power-law scaling at such lags via Extended Self Similarity (ESS), lack of apparent consistency between sample frequency distributions of data and their increments and, in some cases, decay of increment sample frequency tails with increased lag. Existing scaling models capture some but not all of these phenomena in a consistent manner. We describe a new scaling model that does so within a unified theoretical framework which is based on the notion of sub-Gaussian fields subordinated to truncated fractional Brownian motion or truncated fractional Gaussian noise with heavy tailed subordinators. We illustrate our approach on field scale log permeability data.