scholarly journals The Probability Distribution of Sea Surface Wind Speeds. Part I: Theory and SeaWinds Observations

2006 ◽  
Vol 19 (4) ◽  
pp. 497-520 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Surface Wind ◽  
Sea Surface ◽  
Wind Speeds ◽  
Sea Surface Wind ◽  
The Mean

Abstract The probability distribution of sea surface wind speeds, w, is considered. Daily SeaWinds scatterometer observations are used for the characterization of the moments of sea surface winds on a global scale. These observations confirm the results of earlier studies, which found that the two-parameter Weibull distribution provides a good (but not perfect) approximation to the probability density function of w. In particular, the observed and Weibull probability distributions share the feature that the skewness of w is a concave upward function of the ratio of the mean of w to its standard deviation. The skewness of w is positive where the ratio is relatively small (such as over the extratropical Northern Hemisphere), the skewness is close to zero where the ratio is intermediate (such as the Southern Ocean), and the skewness is negative where the ratio is relatively large (such as the equatorward flank of the subtropical highs). An analytic expression for the probability density function of w, derived from a simple stochastic model of the atmospheric boundary layer, is shown to be in good qualitative agreement with the observed relationships between the moments of w. Empirical expressions for the probability distribution of w in terms of the mean and standard deviation of the vector wind are derived using Gram–Charlier expansions of the joint distribution of the sea surface wind vector components. The significance of these distributions for improvements to calculations of averaged air–sea fluxes in diagnostic and modeling studies is discussed.

The Probability Distribution of Sea Surface Wind Speeds. Part II: Dataset Intercomparison and Seasonal Variability

2006 ◽  
Vol 19 (4) ◽  
pp. 521-534 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Standard Deviation ◽  
Wind Speed ◽  
Probability Distribution ◽  
Surface Wind ◽  
Surface Wind Speed ◽  
Sea Surface ◽  
Leading Order ◽  
Statistical Structure ◽  
Wind Speeds ◽  
Sea Surface Wind

Abstract The statistical structure of sea surface wind speeds is considered, both in terms of the leading-order moments (mean, standard deviation, and skewness) and in terms of the parameters of a best-fit Weibull distribution. An intercomparison is made of the statistical structure of sea surface wind speed data from four different datasets: SeaWinds scatterometer observations, a blend of Special Sensor Microwave Imager (SSM/I) satellite observations with ECMWF analyses, and two reanalysis products [NCEP–NCAR and 40-yr ECMWF Re-Analysis (ERA-40)]. It is found that while the details of the statistical structure of sea surface wind speeds differs between the datasets, the leading-order features of the distributions are consistent. In particular, it is found in all datasets that the skewness of the wind speed is a concave upward function of the ratio of the mean wind speed to its standard deviation, such that the skewness is positive where the ratio is relatively small (such as over the extratropical Northern Hemisphere), the skewness is close to zero where the ratio is intermediate (such as the Southern Ocean), and the skewness is negative where the ratio is relatively large (such as the equatorward flank of the subtropical highs). This relationship between moments is also found in buoy observations of sea surface winds. In addition, the seasonal evolution of the probability distribution of sea surface wind speeds is characterized. It is found that the statistical structure on seasonal time scales shares the relationships between moments characteristic of the year-round data. Furthermore, the seasonal data are shown to depart from Weibull behavior in the same fashion as the year-round data, indicating that non-Weibull structure in the year-round data does not arise due to seasonal nonstationarity in the parameters of a strictly Weibull time series.

Empirical Models of the Probability Distribution of Sea Surface Wind Speeds

2007 ◽  
Vol 20 (23) ◽  
pp. 5798-5814 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Wind Speed ◽  
Probability Distribution ◽  
Maximum Entropy ◽  
Surface Wind ◽  
Empirical Models ◽  
Sea Surface ◽  
Wind Speeds ◽  
Sea Surface Wind ◽  
Non Gaussian ◽  
Vector Wind

Abstract This study considers the probability distribution of sea surface wind speeds, which have historically been modeled using the Weibull distribution. First, non-Weibull structure in the observed sea surface wind speeds (from SeaWinds observations) is characterized using relative entropy, a natural information theoretic measure of the difference between probability distributions. Second, empirical models of the probability distribution of sea surface wind speeds, parameterized in terms of the parameters of the vector wind probability distribution, are developed. It is shown that Gaussian fluctuations in the vector wind cannot account for the observed features of the sea surface wind speed distribution, even if anisotropy in the fluctuations is accounted for. Four different non-Gaussian models of the vector wind distribution are then considered: the bi-Gaussian, the centered gamma, the Gram–Charlier, and the constrained maximum entropy. It is shown that so long as the relationship between the skewness and kurtosis of the along-mean sea surface wind component characteristic of observations is accounted for in the modeled probability distribution, then all four vector wind distributions are able to simulate the observed mean, standard deviation, and skewness of the sea surface wind speeds with an accuracy much higher than is possible if non-Gaussian structure in the vector winds is neglected. The constrained maximum entropy distribution is found to lead to the best simulation of the wind speed probability distribution. The significance of these results for the parameterization of air/sea fluxes in general circulation models is discussed.

Estimation of the Radionuclide Transport by Applying the Mean, the Standard Deviation and the Skewness of Permeability

1996 ◽  
Vol 465 ◽  
Author(s):  
Y. Niibori ◽  
O. Tochiyama ◽  
T. Chida
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Lognormal Distribution ◽  
Heterogeneous Media ◽  
Arithmetic Mean ◽  
Bernoulli Trials ◽  
The Mean ◽  
Independent Parameters

ABSTRACTA new method for estimating the mass transport by using the stochastic values (the arithmetic mean, the standard deviation and the skewness) of permeability is presented. Generally, detail of permeability distribution cannot be obtained except for moments of the distribution. Also, measurement results of permeability for the rock matrix including cracks or fast flowpaths do not always follow the log-normal distribution frequently applied. In such a situation, we must evaluate the characteristic permeabilities for the whole or some regions of the disposal site including the accessible environment.The authors have investigated the characteristic permeability on the basis of some probability density functions of permeability, applying the Monte Carlo method and FEM. It was found that its value does not depend on type of probability density function of permeability, but on the arithmetic mean, the standard deviation and the skewness of permeability [1].This paper describes the use of the stochastic values of permeability for estimating the rate of radioactivity release to the accessible environment, applying the advection-dispersion model to two-dimensional, heterogeneous media. When a discrete probability density function (referred to as ‘the Bernoulli trials’) and the lognormal distribution have common values for the arithmetic mean, the standard deviation and the skewness of permeability, the calculated transport rates (described as the pseudo impulse responses) show good agreements for Peclet number around 10 and the dimensionless standard deviation around 1. Further, it is found that the transport rates apparently depends not only on the arithmetic mean and the standard deviation, but also on the skewness of permeability. When the value of skewness dose not follow the lognormal distribution which has only two independent parameters (the mean and the standard deviation), we can replicate the three moments estimated from an observed distribution of permeability, by using the Bernoulli trials having three independent parameters.

Effects of the Fractional Laplacian Order on the Nonlocal Elastic Rod Response

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Giuseppina Autuori ◽  
Federico Cluni ◽  
Vittorio Gusella ◽  
Patrizia Pucci
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Coefficient Of Variation ◽  
Fractional Laplacian ◽  
Numerical Procedure ◽  
Elastic Rod ◽  
The Mean ◽  
Distributed Forces ◽  
Nonlinear Fashion

In this paper, we yield with a nonlocal elastic rod problem, widely studied in the last decades. The main purpose of the paper is to investigate the effects of the statistic variability of the fractional operator order s on the displacements u of the rod. The rod is supposed to be subjected to external distributed forces, and the displacement field u is obtained by means of numerical procedure. The attention is particularly focused on the parameter s, which influences the response in a nonlinear fashion. The effects of the uncertainty of s on the response at different locations of the rod are investigated by the Monte Carlo simulations. The results obtained highlight the importance of s in the probabilistic feature of the response. In particular, it is found that for a small coefficient of variation of s, the probability density function of the response has a unique well-identifiable mode. On the other hand, for a high coefficient of variation of s, the probability density function of the response decreases monotonically. Finally, the coefficient of variation and, to a small extent, the mean of the response tend to increase as the coefficient of variation of s increases.

scholarly journals The Probability Distribution of Sea Surface Wind Speeds: Effects of Variable Surface Stratification and Boundary Layer Thickness

2010 ◽  
Vol 23 (19) ◽  
pp. 5151-5162 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Surface Wind ◽  
Sea Surface ◽  
Surface Winds ◽  
Free Atmosphere ◽  
Wind Speeds ◽  
Sea Surface Wind ◽  
Variable Surface

Abstract Air–sea exchanges of momentum, energy, and material substances of fundamental importance to the variability of the climate system are mediated by the character of the turbulence in the atmospheric and oceanic boundary layers. Sea surface winds influence, and are influenced by, these fluxes. The probability density function (pdf) of sea surface wind speeds p(w) is a mathematical object describing the variability of surface winds that arises from the physics of the turbulent atmospheric planetary boundary layer. Previous mechanistic models of the pdf of sea surface wind speeds have considered the momentum budget of an atmospheric layer of fixed thickness and neutral stratification. The present study extends this analysis, using an idealized model to consider the influence of boundary layer thickness variations and nonneutral surface stratification on p(w). It is found that surface stratification has little direct influence on p(w), while variations in boundary layer thickness bring the predictions of the model into closer agreement with the observations. Boundary layer thickness variability influences the shape of p(w) in two ways: through episodic downward mixing of momentum into the boundary layer from the free atmosphere and through modulation of the importance (relative to other tendencies) of turbulent momentum fluxes at the surface and the boundary layer top. It is shown that the second of these influences dominates over the first.

scholarly journals Comparison Of Three Numerical Methods For Estimating Weibull Parameters Using Weibull Distribution Model In Nigeria

2020 ◽  
Vol 27 (2) ◽  
pp. 8-15
Author(s):  
J.A. Oyewole ◽  
F.O. Aweda ◽  
D. Oni
Keyword(s):  
Standard Deviation ◽  
Wind Speed ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Accurate Estimation ◽  
Weibull Parameters ◽  
Factor Method ◽  
Deviation Method

There is a crucial need in Nigeria to enhance the development of wind technology in order to boost our energy supply. Adequate knowledge about the wind speed distribution becomes very essential in the establishment of Wind Energy Conversion Systems (WECS). Weibull Probability Density Function (PDF) with two parameters is widely accepted and is commonly used for modelling, characterizing and predicting wind resource and wind power, as well as assessing optimum performance of WECS. Therefore, it is paramount to precisely estimate the scale and shape parameters for all regions or sites of interest. Here, wind data from year 2000 to 2010 for four different locations (Port Harcourt, Ikeja, Kano and Jos) were analysed and the Weibull parameters was determined. The three methods employed are Mean Standard Deviation Method (MSDM), Energy Pattern Factor Method (EPFM) and Method of Moments (MOM) for estimating Weibull parameters. The method that gave the most accurate estimation of the wind speed was MSDM method, while Energy Pattern Factor Method (EPFM) is the most reliable and consistent method for estimating probability density function of wind. Keywords: Weibull Distribution, Method of Moment, Mean Standard Deviation Method, Energy Pattern Method

scholarly journals A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2000
Author(s):  
Domingo Benítez ◽  
Gustavo Montero ◽  
Eduardo Rodríguez ◽  
David Greiner ◽  
Albert Oliver ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Epidemic Model ◽  
Temporal Evolution ◽  
Growth Models ◽  
Model Fit ◽  
Gaussian Probability Density Function ◽  
Spatio Temporal

A novel phenomenological epidemic model is proposed to characterize the state of infectious diseases and predict their behaviors. This model is given by a new stochastic partial differential equation that is derived from foundations of statistical physics. The analytical solution of this equation describes the spatio-temporal evolution of a Gaussian probability density function. Our proposal can be applied to several epidemic variables such as infected, deaths, or admitted-to-the-Intensive Care Unit (ICU). To measure model performance, we quantify the error of the model fit to real time-series datasets and generate forecasts for all the phases of the COVID-19, Ebola, and Zika epidemics. All parameters and model uncertainties are numerically quantified. The new model is compared with other phenomenological models such as Logistic Grow, Original, and Generalized Richards Growth models. When the models are used to describe epidemic trajectories that register infected individuals, this comparison shows that the median RMSE error and standard deviation of the residuals of the new model fit to the data are lower than the best of these growing models by, on average, 19.6% and 35.7%, respectively. Using three forecasting experiments for the COVID-19 outbreak, the median RMSE error and standard deviation of residuals are improved by the performance of our model, on average by 31.0% and 27.9%, respectively, concerning the best performance of the growth models.

scholarly journals A Wind Speed Retrieval Model for Sentinel-1A EW Mode Cross-Polarization Images

2019 ◽  
Vol 11 (2) ◽  
pp. 153 ◽  
Author(s):  
Yuan Gao ◽  
Changlong Guan ◽  
Jian Sun ◽  
Lian Xie
Keyword(s):  
Wind Speed ◽  
Incidence Angle ◽  
Surface Wind ◽  
European Space Agency ◽  
Sea Surface ◽  
Cross Polarization ◽  
Retrieval Model ◽  
Sar Images ◽  
Wind Speeds ◽  
Sea Surface Wind

In contrast to co-polarization (VV or HH) synthetic aperture radar (SAR) images, cross-polarization (CP for VH or HV) SAR images can be used to retrieve sea surface wind speeds larger than 20 m/s without knowing the wind directions. In this paper, a new wind speed retrieval model is proposed for European Space Agency (ESA) Sentinel-1A (S-1A) Extra-Wide swath (EW) mode VH-polarized images. Nineteen S-1A images under tropical cyclone condition observed in the 2016 hurricane season and the matching data from the Soil Moisture Active Passive (SMAP) radiometer are collected and divided into two datasets. The relationships between normalized radar cross-section (NRCS), sea surface wind speed, wind direction and radar incidence angle are analyzed for each sub-band, and an empirical retrieval model is presented. To correct the large biases at the center and at the boundaries of each sub-band, a corrected model with an incidence angle factor is proposed. The new model is validated by comparing the wind speeds retrieved from S-1A images with the wind speeds measured by SMAP. The results suggest that the proposed model can be used to retrieve wind speeds up to 35 m/s for sub-bands 1 to 4 and 25 m/s for sub-band 5.

Age Reporting of Very Old Samples

Radiocarbon ◽  
1980 ◽  
Vol 22 (4) ◽  
pp. 1021-1027 ◽  
Author(s):  
Adam Walanus ◽  
Mieczysław F Pazdur
Keyword(s):  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Statistical Interpretation ◽  
Very Old ◽  
Radiocarbon Age ◽  
Fiducial Probability ◽  
Limiting Value

Problems of the statistical interpretation of radiocarbon age measurements of old samples are discussed, based on the notion of fiducial probability distribution. A probability density function of age has been given. A detailed discussion of different facets of the probability distribution of age has led us to the confirmation of the use of 2σ as the best limiting value between the regions of finite and infinite dates. It has been proposed to make use of the principle of constant probability P = 0.68 in the regions of both finite and infinite ages instead of the criterion N + kσ.

A New Microcontact Model Developed for Variable Fractal Dimension, Topothesy, Density of Asperity, and Probability Density Function of Asperity Heights

2006 ◽  
Vol 74 (4) ◽  
pp. 603-613 ◽  
Author(s):  
Jeng Luen Liou ◽  
Jen Fin Lin
Keyword(s):  
Fractal Dimension ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Gaussian Distribution ◽  
Fractal Theory ◽  
Radius Of Curvature ◽  
The Mean ◽  
Contact Surfaces ◽  
Non Gaussian

In the present study, the fractal theory is applied to modify the conventional model (the Greenwood and Williamson model) established in the statistical form for the microcontacts of two contact surfaces. The mean radius of curvature (R) and the density of asperities (η) are no longer taken as constants, but taken as variables as functions of the related parameters including the fractal dimension (D), the topothesy (G), and the mean separation of two contact surfaces. The fractal dimension and the topothesy varied by differing the mean separation of two contact surfaces are completely obtained from the theoretical model. Then the mean radius of curvature and the density of asperities are also varied by differing the mean separation. A numerical scheme is thus developed to determine the convergent values of the fractal dimension and topothesy corresponding to a given mean separation. The topographies of a surface obtained from the theoretical prediction of different separations show the probability density function of asperity heights to be no longer the Gaussian distribution. Both the fractal dimension and the topothesy are elevated by increasing the mean separation. The density of asperities is reduced by decreasing the mean separation. The contact load and the total contact area results predicted by variable D, G*, and η as well as non-Gaussian distribution are always higher than those forecast with constant D, G*, η, and Gaussian distribution.

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