Simulation and analysis of scalable non-Gaussian statistically anisotropic random functions

Monica Riva, Marco Panzeri, Alberto Guadagnini, Shlomo P. Neuman

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Many earth and environmental (as well as other) variables, Y, and their spatial or temporal increments, δ. Y, exhibit non-Gaussian statistical scaling. Previously we were able to capture some key aspects of such scaling by treating Y or δ. Y as standard sub-Gaussian random functions. We were however unable to reconcile two seemingly contradictory observations, namely that whereas sample frequency distributions of Y (or its logarithm) exhibit relatively mild non-Gaussian peaks and tails, those of δ. Y display peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we overcame this difficulty by developing a new generalized sub-Gaussian model which captures both behaviors in a unified and consistent manner, exploring it on synthetically generated random functions in one dimension (Riva et al., 2015). Here we extend our generalized sub-Gaussian model to multiple dimensions, present an algorithm to generate corresponding random realizations of statistically isotropic or anisotropic sub-Gaussian functions and illustrate it in two dimensions. We demonstrate the accuracy of our algorithm by comparing ensemble statistics of Y and δ. Y (such as, mean, variance, variogram and probability density function) with those of Monte Carlo generated realizations. We end by exploring the feasibility of estimating all relevant parameters of our model by analyzing jointly spatial moments of Y and δ. Y obtained from a single realization of Y.

Original languageEnglish (US)
Pages (from-to)88-95
Number of pages8
JournalJournal of Hydrology
StatePublished - Dec 1 2015


  • Generalized sub-Gaussian model
  • Heavy-tailed distributions
  • Parameter estimation
  • Scaling
  • Spatial and ensemble moments

ASJC Scopus subject areas

  • Water Science and Technology


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