Search

Copula functions, which are flexible tools for the derivation of joint probability distributions, have been widely and effectively used to deal with multi variable analysis problems in the field of hydrology and water resources. Particularly in recent decades, this method has received great attention from researchers and engineers because of its advantages in multivariate analysis where the marginals of the data are not normally distributed. This paper provides a state-of-the-art review of the last decade of copula functions in multivariate hydrological frequency analysis, coinci dence and combination analysis of hydrological events, hydrological stochastic simulation, and hydrological modeling and forecasting, etc. More specifically, application issues such as parameter estimation, variable asymmetry, fitting optimization, tail characteristics, multivariable return period selection, and sampling error are described. Finally, the key points and development direction of Copula functions in the field of hydrology and water resources are consid ered, which provides guidance for the application of this method in the future. [ABSTRACT FROM AUTHOR]

Droughts have such essential features as long duration,large scope of influence,and spatio-temporal continuity,and a single variable or double variables were mostly considered in previous studies. By identifying arid patches and judging the continuity between two adjacent droughts based on the given threshold,a spatio-temporally continuous 3D identification method has been proposed for drought events,measuring a drought event in terms of 5 characteristic variables of duration,area,severity,intensity,and central location;the duration-area-severity frequency analysis method based on Copula function has been proposed. Taking Southwest China as an example,SPI drought indices are used to identify the drought events that lasted 3 months or longer in recent 52 years,which totaled 78. Among them,the most serious event from Aug. 2009 to Jun. 2010 has a recurrence period of 94 years. The comparison between the probability distribution function and the Copula function indicates that the 3 characteristic variables of duration,area and severity shall be simultaneously considered upon frequency analysis of drought events. [ABSTRACT FROM AUTHOR]

To predict the surface roughness in machining process, the nonlinear correlation between common monitoring parameters of cutting force and surface roughness should be quantitatively described. The sample values of cutting force and the surface roughness were obtained by turning 7075 high strength aluminum alloy by control variable method. The marginal distribution functions were established, and the multivariate joint distribution function was constructed by the optimized Copula function. Based on the Copula function theory and the joint function model, the global, local and tail relationship between cutting force and surface roughness was analyzed. The results show that the cutting force has obviously positive correlation with surface roughness. The correlation structure is centrosymmetric, and the correlation degrees at the both ends are larger than that at the center. The tail correlation coefficient tends to zero, which illuminates that the tail correlation degree is small. [ABSTRACT FROM AUTHOR]