Related papers: Universality and Scale Invariance in Hourly Rainfa…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
We analyze the statistics of water droplet avalanches in a continuously driven system. Distributions are obtained for avalanche size, lifetime, and time between successive avalanches, along with power spectra and return maps. For low flow…
We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
Based on extensive air shower simulations it is shown that the electron distributions with respect to the two angles, determining electron direction at a given shower age, for a fixed electron energy and lateral distance, are universal. It…
Power-law type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constrains that limit the power-law range for the distributions…
The interevent time distribution characterizes the temporal occurrence in seismic catalogs. Universal scaling properties of this distribution have been evidenced for entire catalogs and seismic sequences. Recently, these universal features…
The general circulation of the atmosphere (GCA) carries out a constant and unidirectional transfer of air masses, therefore its influence is manifested in the distribution of precipitation around the globe due to the occurrence of rain…
We investigate flow dynamics in rivers characterized by basin areas and daily mean discharge spanning different orders of magnitude. We show that the delayed increments evaluated at time scales ranging from days to months can be opportunely…
The paper presents improved mathematical models and methods for statistical regularities in the behavior of some important characteristics of precipitation: duration of a wet period, maximum daily and total precipitation volumes within a…
Taylor's power law (TL) or fluctuation scaling has been verified empirically for the abundances of many species, human and non-human, and in many other fields including physics, meteorology, computer science, and finance. TL asserts that…
The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of…
The classic meteorological law of diffusion in the atmosphere was given experimentally, by Richardson in 1926, whose result that the mean squared distance <R^2>=cT^3, the time cubed, is in accord with the scaling theory of Komogorov […
We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities vm during avalanches described by the mean field theory of the interface depinning transition. In…
Taylors Law (TL) describes the scaling relationship between the mean and variance of populations as a power-law. TL is widely observed in ecological systems across space and time with exponents varying largely between 1 and 2. Many…
Numerous weather parameters affect the occurrence and amount of rainfall. Therefore, it is important to study these parameters and their interdependency. In this paper, different weather and time-related variables -- relative humidity,…
Robust sensing and perception in adverse weather conditions remain one of the biggest challenges for realizing reliable autonomous vehicle mobility services. Prior work has established that rainfall rate is a useful measure for the…
We consider daily rainfall observations at 32 stations in the province of North Holland (the Netherlands) during 30 years. Let $T$ be the total rainfall in this area on one day. An important question is: what is the amount of rainfall $T$…
In a recent paper, we have reported a universal power law for both site and bond percolation thresholds for any lattice of cubic symmetry. Extension to anisotropic lattices is discussed.
A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon…