Joint probability of storm surge and wave along Hainan Island based on bi-variate copulas analysis

2020 ◽  
Author(s):  
Meng Cheng ◽  
Weihua Fang
Keyword(s):  
Probability Distribution ◽  
Storm Surge ◽  
Wave Height ◽  
Significant Wave Height ◽  
Probability Distributions ◽  
Joint Probability ◽  
Hainan Island ◽  
Joint Probability Distribution ◽  
Significant Wave ◽  
Surge Height

<p>Tropical cyclones (TCs) often bring multiple hazards to offshore and onshore areas, including wind, rainfall, riverine flood, wave and storm surge. These hazards usually interact with each other and cause greater amplified hazard intensity. In the coastal areas, wave may damage coastal defense system like sea walls and dykes, and overtopping storm surge could hence become severe flooding due to the breach of the dykes. The probability distributions of wave and surge, as univariate respectively, have been studies and used in the design in various research. However, far less investigations on their joint probability distribution have been carried out in the past.</p><p>In this study, the dataset of hourly surge height, and significant wave height of 89 TC events impacting along Hainan Island during 1949~2013 was obtained, which are simulated numerically with ADCIRC and SWAN respectively. Following that, 4 types of probability distributions for univariate were used to fit the marginal distribution of storm surge and wave. Secondly, Frank, Clayton and Gumbel Copula were tried to construct the joint probability distribution of wave and surge, and the optimal Copula was determined by K-S test and AIC, BIC criteria. Based on the optimal Copula selected for each area of interest, the joint return period of wave and surge was estimated.</p><p>The results show that, 1) the annual maximum value of the storm surge height and significant wave height of Hainan Island has a relatively obvious geographical distribution regularity. 2) GEV and Gumbel are the most optimal distribution for storm surge height and significant wave height respectively. 3) Clayton Copula is the best model for fitting joint probability of storm surge and wave. The estimated joining probability distribution can help the determination of design standard, and typical TC disaster scenario development.</p>

Statistical Uncertainty in Long-Term Distributions of Significant Wave Height

1996 ◽  
Vol 118 (4) ◽  
pp. 284-291 ◽  
Author(s):  
C. Guedes Soares ◽  
A. C. Henriques
Keyword(s):  
Probability Distribution ◽  
Wave Height ◽  
Significant Wave Height ◽  
Data Sets ◽  
Monthly Basis ◽  
Significant Wave ◽  
Fitting Procedure ◽  
The One ◽  
Homogeneous Data

This work examines some aspects involved in the estimation of the parameters of the probability distribution of significant wave height, in particular the homogeneity of the data sets and the statistical methods of fitting a distribution to data. More homogeneous data sets are organized by collecting the data on a monthly basis and by separating the simple sea states from the combined ones. A three-parameter Weibull distribution is fitted to the data. The parameters of the fitted distribution are estimated by the methods of maximum likelihood, of regression, and of the moments. The uncertainty involved in estimating the probability distribution with the three methods is compared with the one that results from using more homogeneous data sets, and it is concluded that the uncertainty involved in the fitting procedure can be more significant unless the method of moments is not considered.

scholarly journals Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging

2019 ◽  
Vol 23 ◽  
pp. 271-309
Author(s):  
Joseph Muré
Keyword(s):  
Probability Distribution ◽  
Gibbs Sampler ◽  
Prediction Interval ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Conditional Distributions ◽  
Stationary Probability Distribution ◽  
Gibbs Sampling Algorithm ◽  
Correlation Parameters

Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates them. When they are compatible, a Gibbs sampler can be used to sample from this joint distribution. When they are not, the Gibbs sampling algorithm may still be applied, resulting in a “pseudo-Gibbs sampler”. We show its stationary probability distribution to be the optimal compromise between the conditional distributions, in the sense that it minimizes a mean squared misfit between them and its own conditional distributions. This allows us to perform Objective Bayesian analysis of correlation parameters in Kriging models by using univariate conditional Jeffreys-rule posterior distributions instead of the widely used multivariate Jeffreys-rule posterior. This strategy makes the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage.

scholarly journals Tests for quantum contextuality in terms of Q-entropies

2014 ◽  
Vol 14 (11&12) ◽  
pp. 996-1013
Author(s):  
Alexey E. Rastegin
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Theoretic Approach ◽  
Entropic Inequalities ◽  
Information Theoretic ◽  
The Family ◽  
Information Theoretic Approach ◽  
New Inequalities

The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and noncontextuality notions are usually treated with use of the so-called marginal scenarios. These hypotheses lead to the existence of a joint probability distribution, which marginalizes to all particular ones. Assuming the existence of such a joint probability distribution, we derive the family of inequalities of Bell's type in terms of conditional $q$-entropies for all $q\geq1$. Quantum violations of the new inequalities are exemplified within the Clauser--Horne--Shimony--Holt (CHSH) and Klyachko--Can--Binicio\v{g}lu--Shumovsky (KCBS) scenarios. An extension to the case of $n$-cycle scenario is briefly mentioned. The new inequalities with conditional $q$-entropies allow to expand a class of probability distributions, for which the nonlocality or contextuality can be detected within entropic formulation. The $q$-entropic inequalities can also be useful in analyzing cases with detection inefficiencies. Using two models of such a kind, we consider some potential advantages of the $q$-entropic formulation.

The joint probability distribution function of structure factors with rational indices. IV. The P1 case

1999 ◽  
Vol 55 (3) ◽  
pp. 512-524
Author(s):  
Carmelo Giacovazzo ◽  
Dritan Siliqi ◽  
Cristina Fernández-Castaño
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Joint Probability ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Joint Probability Distribution ◽  
Structure Factors ◽  
Joint Probability Distributions ◽  
The Hilbert Transform

The method of the joint probability distribution functions of structure factors has been extended to reflections with rational indices. The most general case, space group P1, has been considered. The positional parameters are the primitive random variables of our probabilistic approach, while the reflection indices are kept fixed. Quite general joint probability distributions have been considered from which conditional distributions have been derived: these proved applicable to the accurate estimation of the real and imaginary parts of a structure factor, given prior information on other structure factors. The method is also discussed in relation to the Hilbert-transform techniques.

Implications of nearshore processes on the significant wave height probability distribution

2008 ◽  
Vol 46 (sup2) ◽  
pp. 303-313 ◽  
Author(s):  
Daniel González-Marco ◽  
Rodolfo Bola˜os ◽  
Jose Maria Alsina ◽  
Agustin Sánchez-Arcilla
Keyword(s):  
Probability Distribution ◽  
Wave Height ◽  
Significant Wave Height ◽  
Nearshore Processes ◽  
Significant Wave

scholarly journals Analytical theory of turbulent diffusion

1961 ◽  
Vol 11 (2) ◽  
pp. 257-283 ◽  
Author(s):  
P. H. Roberts
Keyword(s):  
Probability Distribution ◽  
Turbulent Diffusion ◽  
Similarity Theory ◽  
Probability Distributions ◽  
Joint Probability ◽  
Relative Displacement ◽  
Initial Position ◽  
Joint Probability Distribution ◽  
Variable Diffusion ◽  
High Reynolds

Recently Kraichnan (1959) has propounded a theory of homogeneous turbulence, based on a novel perturbation method, that leads to closed equations for the velocity covariance. In the present paper, this method is applied to the theory of turbulent diffusion and closed equations are derived for the probability distributions of the positions of marked fluid elements released in a turbulent flow.Two topics are discussed in detail. The first is the probability distribution, at timet, of the displacement of an element from its initial position. In homogeneous flows, this distribution is found to resemble that for classical diffusion but with a variable coefficient of diffusion which is proportional to$v^2_0 t$for$t \ll l|v_0$and which approaches a constant value [eDot ]lv0fortt[Gt ]l/v0(l= macroscale,v0= r.m.s. turbulent velocity).The second topic treated is the joint probability distribution of the displacements of two fluid elements. Particular attention is focused upon the probability distribution of relative displacement, i.e. Richardson's distance-neighbour function. This is found to be Gaussian for separationsrwhich are large ([Gt ]l). For smaller separations (r[Lt ]l), its behaviour at high Reynolds numbers is found to be quite well expressed in terms of a variable diffusion coefficientK(r,t), as suggested by Richardson (1926). For all but extremely short times,K(r,t) is found to depend only onrand on the form of the inertial range spectrumE(k). On assuming$E(r) \propto v^2_0 l(kl)^{- \frac {3}{2}}$as results from Kraichnan's approximation (1959), one finds$E(r) \propto v_0 l(r|l)^{ \frac {3}{2}}$. On the basis of similarity arguments of the Kolmogorov type, which give$E(r) \propto v^2_0 l(kl)^{- \frac {5}{2}}$, one finds$E(r) \propto v_0 l(r|l)^{ \frac {4}{3}}$as, in fact, Richardson originally proposed. The dispersionr2is proportional to$l^2(v_0 t|l)^4$on Kraichnan's theory; while$\langle r^2 \rangle \propto l^2 (v_0 t|l)^3$on the similarity theory. This illustrates that the behaviour of$\langle r^2 \rangle$is very sensitive to the spectrum.

scholarly journals Bayesian Wind Speed Estimation Conditioned on Significant Wave Height for GNSS-R Ocean Observations

2017 ◽  
Vol 34 (6) ◽  
pp. 1193-1202 ◽  
Author(s):  
Maria Paola Clarizia ◽  
Christopher S. Ruf
Keyword(s):  
Wind Speed ◽  
Wave Height ◽  
Significant Wave Height ◽  
Joint Probability ◽  
Satellite System ◽  
Bayesian Estimator ◽  
Significant Wave ◽  
Wind Speeds ◽  
Speed Estimator ◽  
Low Wind Speeds

AbstractSpaceborne Global Navigation Satellite System reflectometry observations of the ocean surface are found to respond to components of roughness forced by local winds and to a longer wave swell that is only partially correlated with the local wind. This dual sensitivity is largest at low wind speeds. If left uncorrected, the error in wind speeds retrieved from the observations is strongly correlated with the significant wave height (SWH) of the ocean. A Bayesian wind speed estimator is developed to correct for the long-wave sensitivity at low wind speeds. The approach requires a characterization of the joint probability of occurrence of wind speed and SWH, which is derived from archival reanalysis sea-state records. The Bayesian estimator is applied to spaceborne data collected by the Technology Demonstration Satellite-1 (TechDemoSat-1) and is found to provide significant improvement in wind speed retrieval at low winds, relative to a conventional retrieval that does not account for SWH. At higher wind speeds, the wind speed and SWH are more highly correlated and there is much less need for the correction.

scholarly journals STATISTICAL MODELLING OF LONG-TERM WAVE CLIMATES

1986 ◽  
Vol 1 (20) ◽  
pp. 4 ◽  
Author(s):  
Richard Burrows ◽  
Barham A. Salih
Keyword(s):  
Data Base ◽  
Wave Height ◽  
Significant Wave Height ◽  
Joint Probability ◽  
Statistical Modelling ◽  
Wave Climate ◽  
Statistical Properties ◽  
Significant Wave ◽  
Wave Data

The paper discusses the long-term statistical properties of ocean and coastal wave climates derived from the analysis of instrumental wave data. The aim of the work reported has been to determine the theoretical distributions, from those commonly used in analysis of wave data, which best describe the joint probability of significant wave height, Hs, and mean zero-upcrossing period, Tz. A method of modelling the wave climate in this manner has been developed utilizing parametric means of specification. The data base used in the study covers records from 18 sites around the British Isles.

CHECKERBOARD COPULAS OF MAXIMUM ENTROPY WITH PRESCRIBED MIXED MOMENTS

2018 ◽  
Vol 107 (3) ◽  
pp. 302-318
Author(s):  
JONATHAN BORWEIN ◽  
PHIL HOWLETT
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Marginal Distributions ◽  
Joint Probability Distributions

In modelling joint probability distributions it is often desirable to incorporate standard marginal distributions and match a set of key observed mixed moments. At the same time it may also be prudent to avoid additional unwarranted assumptions. The problem is to find the least ordered distribution that respects the prescribed constraints. In this paper we will construct a suitable joint probability distribution by finding the checkerboard copula of maximum entropy that allows us to incorporate the appropriate marginal distributions and match the nominated set of observed moments.

scholarly journals Coastal Impacts of Storm Gloria (January 2020) over the Northwestern Mediterranean

2020 ◽  
Author(s):  
Angel Amores ◽  
Marta Marcos ◽  
Diego S. Carrió ◽  
Lluís Gómez-Pujol
Keyword(s):  
Storm Surge ◽  
Wave Height ◽  
Significant Wave Height ◽  
Wind Waves ◽  
Storm Surges ◽  
Western Mediterranean ◽  
Eastern Coast ◽  
Historical Records ◽  
Significant Wave ◽  
Coastal Impacts

Abstract. The ocean component and coastal impacts of Storm Gloria, that hit the Western Mediterranean between January 20th and 23rd 2020 are investigated with a numerical simulation of the storm surges and wind-waves. Storm Gloria caused severe damages and beat several historical records such as significant wave height or 24-h accumulated precipitation. The storm surge developed along the eastern coasts of the Iberian Peninsula reached values up to 1 m, and were accompanied by wind-waves with significant wave height up to 8 m. Along the coasts of the Balearic Islands, the storm footprint was characterised by a negligible storm surge and the impacts were caused by large waves. The comparison to historical records reveals that Storm Gloria is one of the most intense among the events in the region during the last decades and that the waves direction was particularly unusual. Our simulation permits quantifying the role of the different forcings in generating the storm surge. Also, the high spatial grid resolution down to 30 m over the Ebro Delta, allows determining the extent of the flooding caused by the storm surge. We also simulate the overtopping caused by high wind waves that affected a rocky coast of high cliffs (~ 15 m) in the eastern coast of Mallorca Island.

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