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• Pairwise coupling of Nataf-based stochastic models through disaggregation. • Generation of multi-scale timeseries with any distribution and correlation structure. • Applicable for multivariate disaggregation/simulation problems. The generation of hydrometeorological time series that exhibit a given probabilistic and stochastic behavior across multiple temporal levels, traditionally expressed in terms of specific statistical characteristics of the observed data, is a crucial task for risk-based water resources studies, and simultaneously a puzzle for the community of stochastics. The main challenge stems from the fact that the reproduction of a specific behavior at a certain temporal level does not imply the reproduction of the desirable behavior at any other level of aggregation. In this respect, we first introduce a pairwise coupling of Nataf-based stochastic models within a disaggregation scheme, and next we propose their puzzle-type configuration to provide a generic stochastic simulation framework for multivariate processes exhibiting any distribution and any correlation structure. Within case studies we demonstrate two characteristic configurations, i.e., a three-level one, operating at daily, monthly and annual basis, and a two-level one to disaggregate daily to hourly data. The first configuration is applied to generate correlated daily rainfall and runoff data at the river basin of Achelous, Western Greece, which preserves the stochastic behavior of the two processes at the three temporal levels. The second configuration disaggregates daily rainfall, obtained from a meteorological station at Germany, to hourly. The two studies reveal the ability of the proposed framework to represent the peculiar behavior of hydrometeorological processes at multiple temporal resolutions, as well as its flexibility on formulating generic simulation schemes. [ABSTRACT FROM AUTHOR]

Geostatistical analysis has been introduced over half a century ago to allow quantifying seemingly random spatial variations in earth quantities such as rock mineral content or permeability. The traditional approach has been to view such quantities as multivariate Gaussian random functions characterized by one or a few well-defined spatial correlation scales. There is, however, mounting evidence that many spatially varying quantities exhibit non-Gaussian behavior over a multiplicity of scales. The purpose of this minireview is not to paint a broad picture of the subject and its treatment in the literature. Instead, we focus on very recent advances in the recognition and analysis of this ubiquitous phenomenon, which transcends hydrology and the Earth sciences, brought about largely by our own work. In particular, we use porosity data from a deep borehole to illustrate typical aspects of such scalable non-Gaussian behavior, describe a very recent theoretical model that (for the first time) captures all these behavioral aspects in a comprehensive manner, show how this allows generating random realizations of the quantity conditional on sampled values, point toward ways of incorporating scalable non-Gaussian behavior in hydrologic analysis, highlight the significance of doing so, and list open questions requiring further research. [ABSTRACT FROM AUTHOR]

For many stochastic phenomena, we observe statistical distributions that have fat-tails and high-peaks compared to the Gaussian distribution. In this paper, we will explain how observable statistical distributions in the macroscopic world could be related to the randomness in the subatomic world. We show that fat-tailed (leptokurtic) phenomena in our everyday macroscopic world are ultimately rooted in Gaussian – or very close to Gaussian-distributed subatomic particle randomness, but they are not, in a strict sense, Gaussian distributions. By running a truly random experiment over a three and a half-year period, we observed a type of random behavior in trillions of photons. Combining our results with simple logic, we find that fat-tailed and high-peaked statistical distributions are exactly what we would expect to observe if the subatomic world is quantized and not continuously divisible. We extend our analysis to the fact that one typically observes fat-tails and high-peaks relative to the Gaussian distribution in stocks and commodity prices and many aspects of the natural world; these instances are all observable and documentable macro phenomena that strongly suggest that the ultimate building blocks of nature are discrete (e.g. they appear in quanta). [ABSTRACT FROM AUTHOR]

The impact of the logconductivity ( Y = ln K ) distribution f Y on transport at the MADE site is analyzed. Our principal interest is in non-Gaussian f Y characterized by heavier tails than the Gaussian. Both the logconductivity moments and f Y itself are inferred, taking advantage of the detailed measurements of Bohling et al. (2012). The resulting logconductivity distribution displays heavier tails than the Gaussian, although the departure from Gaussianity is not significant. The effect of the logconductivity distribution on the breakthrough curve (BTC) is studied through an analytical, physically based model. It is found that the non-Gaussianity of the MADE logconductivity distribution does not strongly affect the BTC. Counterintuitively, assuming heavier tailed distributions for Y , with same variance, leads to BTCs which are more symmetrical than those for the Gaussian f Y , with less pronounced preferential flow. Results indicate that the impact of strongly non-Gaussian, heavy tailed distributions on solute transport in heterogeneous porous formations can be significant, especially in the presence of high heterogeneity, resulting in reduced preferential flow and retarded peak arrivals. [ABSTRACT FROM AUTHOR]

Abstract: Atmospheric dispersion is a complex nonlinear physical process with numerous uncertainties in model parameters, inputs, source parameters, initial and boundary conditions. Accurate propagation of these uncertainties through the dispersion models is crucial for a reliable prediction of the probability distribution of the states and assessment of risk. A simple three-dimensional Gaussian puff-based dispersion model is used as a test case to study the effect of uncertainties in the model parameters and initial conditions on the output concentration. A polynomial chaos based approach is used to numerically investigate the evolution of the model output uncertainties due to initial condition and parametric uncertainties. The polynomial chaos solution is found to be an accurate approximation to ground truth, established by Monte Carlo simulation, while offering an efficient computational approach for large nonlinear systems with a relatively small number of uncertainties. [Copyright &y& Elsevier]

Abstract: Temperature maps of the cosmic microwave background (CMB) radiation, as those obtained by the Wilkinson microwave anisotropy probe (WMAP), provide one of the most precise data sets to test fundamental hypotheses of modern cosmology. One of these issues is related to the statistical properties of the CMB temperature fluctuations. We analysed here the WMAP data and found that the distribution of the CMB temperature fluctuations can be quite well fitted by the anomalous temperature distribution emerging within non-extensive statistical mechanics. This theory is based on the non-extensive entropy , with the Boltzmann–Gibbs expression as the limit case . For the frequencies investigated (, 60.8, and 93.5 GHz), we found that is well described by , with , which indicate, at the 99% confidence level, that Gaussian temperature distributions , corresponding to the limit, do not properly represent the CMB temperature fluctuations measured by WMAP. [Copyright &y& Elsevier]

The distribution of resistance fluctuations of conducting thin films with granular structure near electrical breakdown is studied by numerical simulations. The film is modeled as a resistor network in a steady state determined by the competition between two biased processes, breaking and recovery. Systems of different sizes and with different levels of internal disorder are considered. Sharp deviations from a Gaussian distribution are found near breakdown and the effect increases with the degree of internal disorder. We show that in general this non-Gaussianity is related to the finite size of the system and vanishes in the large size limit. Nevertheless, near the critical point of the conductor–insulator transition, deviations from Gaussianity persist when the size is increased and the distribution of resistance fluctuations is well fitted by the universal Bramwell–Holdsworth–Pinton distribution. [Copyright &y& Elsevier]

In this paper, we perform molecular dynamics (MD) simulations to study the random packing of spheres with different particle size distributions. In particular, we deal with non-Gaussian distributions by means of the Lévy distributions. The initial positions as well as the radii of five thousand non-overlapping particles are assigned inside a confining rectangular box. After that, the system is allowed to settle under gravity towards the bottom of the box. Both the translational and rotational movements of each particle are considered in the simulations. In order to deal with interacting particles, we take into account both the contact and long-range cohesive forces. The normal viscoelastic force is calculated according to the nonlinear Hertz model, whereas the tangential force is calculated through an accurate nonlinear-spring model. Assuming a molecular approach, we account for the long-range cohesive forces using a Lennard-Jones (LJ)-like potential. The packing processes are studied assuming different long-range interaction strengths. • Packing dynamics is sensitive to both the distribution type and long-range forces. • The packing density gradually decays as the ε values increase. • The mean coordination number gradually decays as the ε values increase. • The Lévy type II distribution yields the highest packing densities. [ABSTRACT FROM AUTHOR]