Maximum likelihood environmental calibration and the compute program WACALIB a correction

A recently discovered error in the part of the computer program WACALIB that implements maximum likelihood (ML) calibration has been discovered and corrected. The new version of WACALIB has been re-run with all the data-sets from which results based on the earlier version of WACALIB had been published. The new results suggest that ML regression and calibration perform as well or even better than weighted averaging (WA), at least when judged by the apparent root mean squared error. Further work involving cross-validation is required to evaluate more fully the relative performance of WA and ML approaches.     

An extreme value analysis of the flow of Burbage Brook

An extreme value analysis of the flow of Burbage Brook is carried out by modelling peaks over a high threshold. The aims are to illustrate recently developed statistical techniques and to report on interesting features of the flow of the brook over a 58-year period. Peak flows are found to show marked seasonal variation and a downward trend. Then-year return level is estimated for various values ofn, and the reliability of the estimates is assessed.     

On solution of the inverse problem for confined aquifer flow via maximum likelihood

Joint estimation of transmissivity (T) and storativity (S) in a confined aquifer is done via maximum likelihood (ML). The differential equation of groundwater flow is discretized by the finite-element method, leading to equation _t+x _t=u _t. Elements of matrices and , as well as estimated covariance matrix of noise termu _t, are functions of T and S. By minimizing the negative loglikelihood function corresponding to discretized groundwater flow equation with respect to T and S, ML estimators are obtained. The ML approach is found to yield accurate estimates of T and S (within 9 and 10% of their actual values, respectively) and showed quadratic convergence in Newton's search technique. Prediction of aquifer response, using ML estimators, results in estimated piezometric heads accurate to ±0.5 m from their actual, exact values. Statistical properties of ML estimators are derived and some basic results for statistical inference are given.     

Approximation of Gaussian spatial autoregressive models for massive regular square tessellation data

Most of the literature to date proposes approximations to the determinant of a positive definite n × n spatial covariance matrix (the Jacobian term) for Gaussian spatial autoregressive models that fail to support the analysis of massive georeferenced data sets. This paper briefly surveys this literature, recalls and refines much simpler Jacobian approximations, presents selected eigenvalue estimation techniques, summarizes validation results (for estimated eigenvalues, Jacobian approximations, and estimation of a spatial autocorrelation parameter), and illustrates the estimation of the spatial autocorrelation parameter in a spatial autoregressive model specification for cases as large as n = 37,214,101. The principal contribution of this paper is to the implementation of spatial autoregressive model specifications for any size of georeferenced data set. Its specific additions to the literature include (1) new, more efficient estimation algorithms; (2) an approximation of the Jacobian term for remotely sensed data forming incomplete rectangular regions; (3) issues of inference; and (4) timing results.     

SHOULD BESTOW MORE PHYSICAL CONNOTATION ON GRAIN SIZE PARAMETER

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Application of bivariate extreme value distribution to flood frequency analysis: a case study of Northwestern Mexico

In Mexico, poverty has forced people to live almost on the water of rivers. This situation along with the occurrence of floods is a serious problem for the local governments. In order to protect their lives and goods, it is very important to account with a mathematical tool that may reduce the uncertainties in computing the design events for different return periods. In this paper, the Logistic model for bivariate extreme value distribution with Weibull-2 and Mixed Weibull marginals is proposed for the case of flood frequency analysis. A procedure to estimate their parameters based on the maximum likelihood method is developed. A region in Northwestern Mexico with 16 gauging stations has been selected to apply the model and regional at-site quantiles were estimated. A significant improvement occurs, measured through the use of a goodness-of-fit test, when parameters are estimated using the bivariate distribution instead of its univariate counterpart. Results suggest that it is very important to consider the Mixed Weibull distribution and its bivariate option when analyzing floods generated by a␣mixture of two populations.     

等弧长法及其在土钉墙整体稳定分析中的应用

在利用条分法进行土钉墙整体稳定分析中,采用等弧长法将滑动面以上土体分成若干个等弧长的竖直土条.在此基础上,提出了土钉墙整体稳定安全系数与岩土参数、支护参数、地面附加荷载分布状态、基坑开挖深度及滑动圆圆心坐标之间的函数解析表达式.编制了应用程序并给出了工程实例.     

Selection between the generalized Pareto and kappa distributions in peaks-over-threshold hydrological frequency modelling

Hydrologists use the generalized Pareto (GP) distribution in peaks-over-threshold (POT) modelling of extremes. A model with similar uses is the two-parameter kappa (KAP) distribution. KAP has had fewer hydrological applications than GP, but some studies have shown it to merit wider use. The problem of choosing between GP and KAP arises quite often in frequency analyses. This study, by comparing some discrimination methods between these two models, aims to show which method(s) is (are) recommended. Three specific methods are considered: one uses the Anderson-Darling goodness-of-fit (GoF) statistic, another uses the ratio of maximized likelihood (closely related to the Akaike information criterion and the Bayesian information criterion), and the third employs a normality transformation followed by application of the Shapiro-Wilk statistic. We show this last method to be the most recommendable, due to its advantages with sizes typically encountered in hydrology. We apply the simulation results to some flood POT datasets.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR E. Volpi     

2016年新疆呼图壁6.2级地震前b值异常特征研究

利用2009年以来中国地震台网中心地震编目资料,以2016年新疆呼图壁6.2级地震作为研究对象,采用最大似然法进行b值空间扫描计算,获取震前震中及其邻区地震b值的空间图像。研究结果显示,2016年呼图壁6.2级地震发生在震前显著低b值区域,该异常特征可能反映了地震孕育的应力积累过程,印证了b值的物理意义。