A note on the applicability of log-Gumbel and log-logistic probability distributions in hydrological analyses: I. Known pdf

Abstract

Two probability density functions (pdf), popular in hydrological analyses, namely the log-Gumbel (LG) and log-logistic (LL), are discussed with respect to (a) their applicability to hydrological data and (b) the drawbacks resulting from their mathematical properties. This paper—the first in a two-part series—examines a classical problem in which the considered pdf is assumed to be the true distribution. The most significant drawback is the existence of the statistical moments of LG and LL for a very limited range of parameters. For these parameters, a very rapid increase of the skewness coefficient, as a function of the coefficient of variation, is observed (especially for the log-Gumbel distribution), which is seldom observed in the hydrological data. These probability distributions can be applied with confidence only to extreme situations. For other cases, there is an important disagreement between empirical data and theoretical distributions in their tails, which is very important for the characterization of the distribution asymmetry. The limited range of shape parameters in both distributions makes the analyses (such as the method of moments), that make use of the interpretation of moments, inconvenient. It is also shown that the often-used L-moments are not sufficient for the characterization of the location, scale and shape parameters of pdfs, particularly in the case where attention is paid to the tail part of probability distributions. The maximum likelihood method guarantees an asymptotic convergence of the estimators beyond the domain of the existence of the first two moments (or L-moments), but it is not sensitive enough to the upper tails shape.     

Appraisal of regional and index flood quantile estimators

Our results illustrate the performance of at-site and regional GEV/PWM flood quantile estimators in regions with different coefficients of variation, degrees of regional heterogeneity, record lengths, and number of sites. Analytic approximations of bias and variance are employed. For realistic GEV distributions and short records, the index-flood quantile estimator performs better than a 2-parameter GEV/PWM quantile estimator with a regional shape parameter, or a 3-parameter at-site GEV/PWM quantile estimator, in both humid and especially in arid regions, as long as the degree of regional heterogeneity is moderate. As regional heterogeneity or record lengths increases, 2-parameter estimators quickly dominate. Flood frequency models that assign probabilities larger than 2% to negative flows are unrealistic; experiments employing such distributions provide questionable results. This appraisal generally demonstrates the value of regionalizing estimators of the shape of a flood distribution, and sometimes the coefficient of variation.     

MOMENT DEFICITS ON THE MAJOR FAULTS AND EARTHQUAKE HAZARD ASSESSMENT IN THE EASTERN HIMALAYAN SYNTAXIS

The Eastern Himalayan Syntaxis(EHS)is a critical region for studying the tectonic evolution of Tibetan plateau, which was affected by the intense seismic activities. We use the theory of moment balance, GPS velocities and historical earthquake records to analyze the moment deficits in the EHS, assess the future seismicity and further to predict the recurrence interval of the 1950 Chayu M_S8.6 earthquake. We first collected multiple sets of GPS velocity fields and combined them to reduce the systematic bias. Then a micro-blocks model, constrained by GPS velocities, was built by TDEFNODE software to simultaneously invert the fault elastic strain parameters and rigid motion parameters based on the grid research and simulated annealing methods. The long-term slip rates on the faults were further estimated by the differential motions between the neighboring blocks. The results show that the nearly NS dextral strike-slip faults, Naga Fault and Sagaing Fault, slip with the average rates of ~10.6 and ~16.6mm/a, which are consistent with the lateral extrusion in the Tibetan plateau. However, the Main Frontal Thrust shows a distinguished sinistral strike-slip feature(6~10mm/a), possibly caused by the NNE pushing from the Indian plate to the Eurasian plate. On the other hand, because the EHS is located in frontal area of the collision between Indian and Eurasian plate, most faults show thrusting feature. The most obvious one is the Mishimi Fault, slipping with the rate of 23.3mm/a, implying that the convergence rate of the Indo-European plates is largely absorbed by this fault. The moment accumulation rate in the EHS is higher than the average rate in the Tibetan plateau and the total moment accumulation is(1.15±0.03)×10²² N·m in the last 200a. About 59.7% and 21.6% of the moment accumulation rate concentrate on the Main Frontal Thrust and Mishimi Fault. Second, we selected the earthquake records occurring on the upper crust since 1800AD to analyze the moment release in the EHS based on the data from the International Seismological Centre, United States Geological Survey, and catalogue of historical strong earthquakes in China and some other previous studies. In addition, the Global Centroid Moment Tensor Project and linear regression method were adopted to estimate the relationship between body wave magnitude(m_b), surface wave magnitude(M_S), local magnitude(M_L)and the moment(M₀). Then we further estimated the total fault moment release in the EHS, (5.50±2.54)×10²¹N·m, which is significantly lower than the total moment accumulation. About 79.2% of the moment release occurs on the Mishimi Fault, this is because the 1950 M_S8.6 Chayu earthquake is assumed to have ruptured on this fault. Finally, the present-day moment deficits on the faults in the EHS were calculated by the differences between the moment accumulation and release, which represent the possibility to produce earthquakes on the upper crust faults in the future. The largest moment deficit was found on the Main Frontal Thrust near Bhutan, which is able to rupture with M_W8.1+. Similarly, earthquakes with M_W7.5+ and M_W7.3+ have the potentials to occur on the Naga Fault and the Jiali Fault near Tongmai. However, the future earthquake scales may be less than M_W7.1 on the remaining faults. Moderate minor earthquakes are the main activity in the area near the Yarlung Zangbo Suture zone and the southern Sagaing Fault. Although the Chayu M_S8.6 earthquake occurred near the Mishimi Fault and the eastern MFT, the earthquake risk on those two faults cannot be ignored. Meanwhile, no matter which fault produced the Chayu earthquake, its recurrence will likely be 660a to 1 030a.     

The effects of closure on the moments of a distribution

When percentages are formed from uncorrelated, normally distributed parent variables the moments of the percentage distribution may differ considerably from those of the parents. Equations can be derived which enable the approximation of the moments of a percentage variable in terms of the moments of the parent distribution, the row sum statistics, and the correlation between a part of a sum and the sum (the part-whole correlation). If the part-whole correlation is negative the mean and variance of the percentage are increased (relative to the means and variances of those variables with a positive part-whole correlation) and the percentage variable will exhibit a positive skewness. If the part-whole correlation is positive the percentage variable will be negatively skewed if, and only if, the part-whole correlation is greater than the ratio of the coefficient of variation of the row sum (T) to the coefficient of variation of the parent variable. The kurtosis of the percentage variable must be greater than that of the parent variable regardless of the sign of the part-whole correlation. It is obvious that the interpretation or explanation of the distribution of a percentage variable must include an assessment of the effects of percentage formation. However, at the present time the isolation of the percentage effect appears to be impossible unless the parent data set is available.     

Simulation of Surface Air Temperature by GCMs,Statistical Downscaling and Weather Generator: Higher-Order Statistical Moments

The third and fourth statistical moments, that is, skewness and kurtosis, are compared for daily maximum temperature in summer and daily minimum temperature in winter between observations, outputs of two global climate models, four versions of statistical downscaling, and weather generator. The comparison is performed at six stations in central Europe. None of the simulation models can be considered as superior to the others. Causes of a good correspondence with and differences from observations are identified e.g. in the treatment of physics in the models, imperfections in physical parameterizations, or a linear transfer of properties from predictors onto predictands in statistical downscaling.     

一种新的运动检测及轮廓追踪方法

构建了基于块区域二阶矩比的三帧差分运动检测模型,应用文献[1]中的核密度估计模型来滤除其中的非运动区域,并采用支持向量聚类实现多目标检测。给出了运动物体轮廓快速追踪的RW算法,该算法不必考虑检测区域内部的细节问题,能够充分利用所检测到的边缘信息,比较符合人眼对轮廓的搜索习惯。最后给出了实验结果。     

论不连序系列样本概率权重矩不偏计算公式

人们普遍认为要从理论上通过数学分析的方法来论证不连序系列样本概率权重矩的偏倚性是很困难的。本文根据次序统计量理论，分析推证了不连序系列样本概率权重矩的不偏计算公式，论证结果具有较重要的理论和实用意义。