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Responses of Fluvial Forms and Processes to Human Actions in the Damodar River Basin
Published in Balai Chandra Das, Sandipan Ghosh, Aznarul Islam, Suvendu Roy, Anthropogeomorphology of Bhagirathi-Hooghly River System in India, 2020
Sandipan Ghosh, Rahaman Ashique Ilahi
Pearson Type III distribution is a skew distribution with limited range in the left direction, usually bell shaped (Griffs et al., 2007; Raghunath, 2011; Sathe et al., 2012). Logarithmic Pearson Type III distribution (LP3) has the advantage of providing a skew adjustment, and if the skew is zero, the log Pearson distribution is identical to the log normal distribution (Vogel and McMartin, 1991; Rao and Hamed, 2000; Stichellout et al., 2006; Raghunath, 2011; Millington et al., 2011; Zakaullah et al., 2012; Whitfield, 2012). The probability density function for type III (with origin at the mode) is f(x)=Fo(1−x/a)cexp(−cx/2)
Process Simulation
Published in Joachim Piprek, Handbook of Optoelectronic Device Modeling and Simulation, 2017
Simon Z. M. Li, Changsheng Xia, Yue Fu
where f1 is the Pearson IV for the surface region and f2 is the Pearson IV for the bulk region. Rp, σp, γp, and β2 are the projected range, standard deviation, skewness, and the kuitosis, respectively, for the first Pearson distribution. Similarly, those with ′ are for the second Pearson function distribution, describing the channeling tail. More details can be found in the works by Park et al. (1990) and Yang et al. (1995).
Numerical formulation based on ocean wave mechanics for offshore structure analysis – a review
Published in Ships and Offshore Structures, 2022
N. A. Mukhlas, N. I. Mohd Zaki, M. K. Abu Husain, S.Z.A. Syed Ahmad, G. Najafian
Srokosz (1998) developed a Pearson distribution that is able to maintain a positive value of skewness and zero kurtosis. Based on the distribution, the maximum and minimum values of surface elevation can be predicted. However, the derivation of the distribution according to the second-order theory is complicated due to the many parameters involved (more than four). Due to the significant interest in the application, Forristall (2000) simplified the distribution using standard statistical tools to describe the short-term distribution wave crest. It was done by fitting a probability distribution to the result of numerical simulations of random waves according to second-order theory. The results have also been compared with the laboratory and several field measurements for the highest crest. Even though the results agree well, the accuracy is still in doubt considering the equipment error in the measurement field test.
Evaluating the utility of remotely sensed soil moisture for the characterization of runoff response over Canadian watersheds
Published in Canadian Water Resources Journal / Revue canadienne des ressources hydriques, 2020
Elené Wadsworth, Catherine Champagne, Aaron A. Berg
The runoff ratio and soil moisture data was tested for normality and homoscedasticity with residual plots in SAS; the data did not fit a normal distribution, violating the assumption of linearity for the Pearson distribution. Therefore, following Crow et al. (2017) the Spearman rank correlation was used as a non-linear measure of correlation strength in Matlab2015Ra. Initially, the SMOS anomaly and absolute weekly soil moisture values were used to compare the resulting strength of the correlations. Exploratory correlations were also calculated at lag times of 1–4 weeks, but these data were not included as the results did not show any improvement over the 1-week soil moisture data sets. SMOS anomalies are only calculated if the pixel unfrozen, therefore the effect of snow covered basins is minimized in the evaluation of soil moisture/runoff relationships.
Modeling Solid Contact between Smooth and Rough Surfaces with Non-Gaussian Distributions
Published in Tribology Transactions, 2019
Tatsunori Tomota, Yasuhiro Kondoh, Toshihide Ohmori
To prepare for asperity distribution calculations, we consider the roughness height distribution of a non-Gaussian rough surface. Several models, including the Pearson distribution, are proposed to consider skewness and kurtosis. However, in this study, we use a Johnson distribution model (Tayebi and Polycarpou (15); Nayak (17)) for convenience. When is the dimensionless roughness height from the mean line of the roughness curve, the roughness height distribution according to the Johnson distribution is where two different formulas are given: the Johnson SU (JSU) distribution SB (JSB) distribution -> Johnson bounded distribution (JSB). We decide which one to use depending on a combination of skewness and kurtosis. Figure 4 shows an overview of the distribution types corresponding to various combinations of skewness and kurtosis (George (18)). and are called the Johnson distribution parameters and are determined by the combination of skewness and kurtosis. Figures 5 and 6 show distributions with various values of skewness and kurtosis. Although Johnson distributions are ideal for representing roughness height distributions, a previous study showed that they coincide well with measured roughness height distributions having characteristic values of skewness and kurtosis (Jeng (19)). Incidentally, the green line of each graph—that is, the line and the line —is equal to the distribution of the Gaussian rough surface (all green lines in the graphs shown later also correspond to the results of the Gaussian rough surface).