Mechanisms and possibilities for the emergence of extreme floods in arid zones (Tiznit plain - Morocco): ميكانزمات واحتمالات نشأة الفيضانات المتطرفة بالمناطق الجافة (سهل تزنيت - المغرب)

In Morocco, the dynamics of change in rainfall patterns have been underway for decades. It is characterized by increasingly frequent and violent hydrological and climatic events (floods and droughts). This work aims to study the peculiarities and mechanisms of the appearance of floods in the watershed of the Oudodou wadi (Province of Tiznit - southwestern Morocco) and conduct a frequency analysis of the extreme hydrological events associated with floods to estimate their probabilities and their return periods. In addition to the diagnosis of natural factors in the area studied and their relationship to the emergence of floods, the methodological approach adopted is divided into two stages. The first, known as historical, is based on the study of 8 flooding cases (1942 - 2014) and the delimitation of threatened areas through the representations of residents. The second step focused on analyzing the frequencies of extreme hydrological events to determine their severity and return periods. Analysis of the results showed that flood thresholds are always associated with the strength and concentration of rainfall, giving them a sudden behavior like summer floods. To guide the interventions of actors in the field, the areas threatened by flooding have been identified according to their degrees of severity. The recurrence of the flows was modeled using the GAMMA law which makes it possible to estimate the probability of occurrence of extreme events (floods) and the instantaneous flows corresponding to the return periods of 2, 5, 10, 20, 50 and 100 years. Biannual and five-year hydrological events correspond to instantaneous flows of 120 and 331 m3/s, while exceptional or even very exceptional cases have a return period of more than 50 and 100 years and correspond to instantaneous flows of 912 and 1035 m3/s.

Application of bayesian scientific approach to constructing the statistical estimations for solving metrological and measurement problems

Nowadays, constructing effective statistical estimates with a limited amount of statistical information constitutes a significant practical problem. The article is devoted to applying the Bayesian scientific approach to the construction of statistical estimates of the parameters of the laws of distribution of random variables. Five distribution laws are considered: The Poisson law, the exponential law, the uniform law, the Pareto law, and the ordinary law. The concept of distribution laws that conjugate with the observed population was introduced and used. It is shown that for considered distribution laws, the parameters of the laws themselves are random variables and obey the typical law, gamma law, gamma - normal law, and Pareto law. Recalculation formulas are obtained to refine the parameters of these laws, taking into account posterior information. If we apply the recalculation formulas several times in a row, we will get some convergent process. Based on a converging process, it is possible to design a process for self-learning a system or self-tuning a system. The developed scientific approach was applied to solve the measuring problems for the testing measuring devices and technical systems. The results of constructing point estimates and constructing interval estimates for these laws' parameters are given. The results of comparison with the corresponding statistical estimates constructed by the classical maximum likelihood method are presented.

Moments estimators and omnibus chi-square tests for some usual probability laws

For many probability laws, in parametric models, the estimation of the parameters can be done in the frame of the maximum likelihood method, or in the frame of moment estimation methods, or by using the plug-in method, etc. Usually, for estimating more than one parameter, the same frame is used. We focus on the moment estimation method in this paper. We use the instrumental tool of the functional empirical process (fep) in Lo (2016) to show how it is practical to derive, almost algebraically, the joint distribution Gaussian law and to derive omnibus chi-square asymptotic laws from it. We choose four distributions to illustrate the method (Gamma law, beta law, Uniform law and Fisher law) and completely describe the asymptotic laws of the moment estimators whenever possible. Simulations studies are performed to investigate for each case the smallest sizes for which the obtained statistical tests are recommendable. Generally, the omnibus chi-square test proposed here work fine with sample sizes around fifty.

Structural properties of generalised Planck distributions

A family of generalised Planck (GP) laws is defined and its structural properties explored. Sometimes subject to parameter restrictions, a GP law is a randomly scaled gamma law; it arises as the equilibrium law of a perturbed version of the Feller mean reverting diffusion; the density functions can be decreasing, unimodal or bimodal; it is infinitely divisible. It is argued that the GP law is not a generalised gamma convolution. Characterisations are obtained in terms of invariance under random contraction of a weighted version of a related law. The GP law is a particular instance of equilibrium laws obtained from a recursion suggested by a genetic mutation-selection balance model. Some related infinitely divisible laws are exhibited.

Location and scale behaviour of the quantiles of a natural exponential family

Let P0 be a probability on the real line generating a natural exponential family (Pt)t∈ℝ. Fix α in (0, 1). We show that the property that Pt((−∞, t)) ≤ α ≤ Pt((−∞, t]) for all t implies that there exists a number μα such that P0 is the Gaussian distribution N(μα, 1). In other terms, if for all t, the number t is a quantile of Pt associated to some threshold α ∈ (0, 1), then the exponential family must be Gaussian. The case α = 1∕2, i.e. when t is always a median of Pt, has been considered in Letac et al. [Statist. Prob. Lett. 133 (2018) 38–41]. Analogously let Q be a measure on [0, ∞) generating a natural exponential family (Q−t)t>0. We show that Q−t([0, t−1)) ≤ α ≤ Q−t([0, t−1]) for all t > 0 implies that there exists a number p = pα > 0 such that Q(dx) ∝ xp−1dx, and thus Q−t has to be a gamma law with parameters p and t.

Analysis of Fracture Networks of the Black Volta Catchment in Côte D’ivoire

A good knowledge of fracturing leads to a better exploitation of the groundwater of the areas in crystalline basement. This study area of interests the catchment of Black Volta area in north eastern Côte d’Ivoire. Its aims to characterize the fracture networks of the catchment of Black Volta. Various methods were used notably mapping using satellite image processing, statistical and geostatistical analysis. The results showed that fracturing of Black Volta area is dense and homogeneous. Statistical analysis of geometric parameter of the fracturing such as fracture lengths and spacing are distributed respectively according to power law and gamma law. The deployment of the fracturing in this area is organized and the experimental variogram is characterized by two nested elementary structures. The practical ranges of these two elementary variograms are respectively 34, 5 km to 60 km. Results indicate that the fracturing of Black Volta area reached a stage of advanced development and is complex. Fracturing of Black Volta area is now well known and the groundwater modeling can be undertaking.

Verification Studies for the Noh Problem Using Nonideal Equations of State and Finite Strength Shocks

The Noh verification test problem is extended beyond the commonly studied ideal gamma-law gas to more realistic equations of state (EOSs) including the stiff gas, the Noble-Abel gas, and the Carnahan–Starling EOS for hard-sphere fluids. Self-similarity methods are used to solve the Euler compressible flow equations, which, in combination with the Rankine–Hugoniot jump conditions, provide a tractable general solution. This solution can be applied to fluids with EOSs that meet criterion such as it being a convex function and having a corresponding bulk modulus. For the planar case, the solution can be applied to shocks of arbitrary strength, but for the cylindrical and spherical geometries, it is required that the analysis be restricted to strong shocks. The exact solutions are used to perform a variety of quantitative code verification studies of the Los Alamos National Laboratory Lagrangian hydrocode free Lagrangian (FLAG).

Testing the impact of stratigraphic uncertainty on spectral analyses of sedimentary series

Spectral analysis is a key tool for identifying periodic patterns in sedimentary sequences, including astronomically related orbital signals. While most spectral analysis methods require equally spaced samples, this condition is rarely achieved either in the field or when sampling sediment core. Here, we propose a method to assess the impact of the uncertainty or error made in the measurement of the sample stratigraphic position on the resulting power spectra. We apply a Monte Carlo procedure to randomise the sample steps of depth series using a gamma distribution. Such a distribution preserves the stratigraphic order of samples and allows controlling the average and the variance of the distribution of sample distances after randomisation. We apply the Monte Carlo procedure on two geological datasets and find that gamma distribution of sample distances completely smooths the spectrum at high frequencies and decreases the power and significance levels of the spectral peaks in an important proportion of the spectrum. At 5 % of stratigraphic uncertainty, a small portion of the spectrum is completely smoothed. Taking at least three samples per thinnest cycle of interest should allow this cycle to be still observed in the spectrum, while taking at least four samples per thinnest cycle of interest should allow its significance levels to be preserved in the spectrum. At 10 and 15 % uncertainty, these thresholds increase, and taking at least four samples per thinnest cycle of interest should allow the targeted cycles to be still observed in the spectrum. In addition, taking at least 10 samples per thinnest cycle of interest should allow their significance levels to be preserved. For robust applications of the power spectrum in further studies, we suggest providing a strong control of the measurement of the sample position. A density of 10 samples per putative precession cycle is a safe sampling density for preserving spectral power and significance level in the Milankovitch band. For lower sampling density, the use of gamma-law simulations should help in assessing the impact of stratigraphic uncertainty in the power spectrum in the Milankovitch band. Gamma-law simulations can also model the distortions of the Milankovitch record in sedimentary series due to variations in the sedimentation rate.

Galactic entropy in extended Kaluza–Klein cosmology

We use a Kaluza–Klein model with variable cosmological and gravitational terms to discuss the nature of galactic entropy function. For this purpose, we assume a universe filled with dark fluid and consider five-dimensional (5D) field equations using the Gamma law equation. We mainly discuss the validity of the first and generalized second laws of galactic thermodynamics for viable Kaluza–Klein models.

Characteristics of the raindrop distributions in RICO shallow cumulus

The physical properties of rain spectra are generally modeled using an analytical distribution. It is common for the gamma distribution and, to a lesser extent, the lognormal distribution to be used. The majority of studies in the literature focusing on the characterization of raindrop distribution are based on deep convective cloud observations, mostly at ground level. This study focuses on shallow-cumulus rain distributions throughout the depth of the cloud layer and subcloud layer using airborne in situ measurements made with both the Particle Measuring Systems (PMS) Optical Array Probe 260X (OAP-260-X) and the PMS two-Dimensional Precipitation (2DP) instruments during the Rain in Cumulus over the Ocean (RICO) field experiment. Sampled spectra analyzed on the scale of large-eddy simulation resolution (100 m) are found to be relatively broad, with values of the shape parameter – υ for the gamma law and σg for the lognormal law – on the order of 1–3 and 1.5–2, respectively. The dependence of the shape parameters on the main rain variables (number concentration, water content, mean volume diameter, sedimentation fluxes and radar reflectivity) is examined, and a parameterization of the shape parameters υ and σg as a function of a power law of the rainwater content and raindrop number concentration is proposed.