Comparative evaluation of Poisson partial duration models for mixed flood populations

Simple homogeneous formulations of two extreme value partial duration flood models are compared to more sophisticated compound formulations in terms of asymptotic performance of quantile estimates. The compound model formulations were developed to model flood series resulting from mixed climatological processes. It was found that only in the case of marked nonhomogeneity in the data samples did the compound formulation of the models offer significant advantages in terms of variance of quantile estimates. However, the estimates from the homogeneous model were significantly biased in the negative direction. This negative bias of quantile estimates from the simple model was even more pronounced when the more sophisticated Weibull model was used as the base.     

Evaluation of risk concepts in partial duration series

Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.     

Evaluation of risk concepts in partial duration series

Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.     

Observed advantage for negative binomial over Poisson distribution in partial duration series

The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds.An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events <-0.1year ^–1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events.     

Observed advantage for negative binomial over Poisson distribution in partial duration series

The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds.An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events <-0.1year ^–1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events.     

On the distribution of flood volume in partial duration series analysis of flood phenomena

A methodology based on the theory of stochastic processes is applied to the analysis of floods. The approach will be based on some results of the theory of extreme values over a threshold. In this paper, we focus on the estimation of the distribution of the flood volume in partial duration series analysis of flood phenomena, by using a bivariate exponential distribution of discharge exceedances and durations over a base level.     

On the distribution of flood volume in partial duration series analysis of flood phenomena

A methodology based on the theory of stochastic processes is applied to the analysis of floods. The approach will be based on some results of the theory of extreme values over a threshold. In this paper, we focus on the estimation of the distribution of the flood volume in partial duration series analysis of flood phenomena, by using a bivariate exponential distribution of discharge exceedances and durations over a base level.     

On the annual maximum distribution in dependent partial duration series

As a basis for development of the annual maximum distribution the so-called partial duration series with Poissonian occurrence times and exponentially distributed peak exceedance values has been selected. The model is generalized by allowing for a Markov dependence between succeeding peak values. Correlation values from p=0 to p=1 can be accounted for by introducing the Marshall-Olkin bivariate exponential distribution, which is presented in detail. The developed distribution function for the annual maximum is throughly analysed and a variety of distribution forms depending on the value of the correlation coefficient and the intensity in the Poisson process is hereby recognized. To a certain extent this might be considered as parallel to the scattering of hydrological regions with different generating mechanisms for the annual maxima.     

Comparative study of flood quantiles estimation by nonparametric models

There are two basic approaches for estimating flood quantiles: a parametric and a nonparametric method. In this study, the comparisons of parametric and nonparametric models for annual maximum flood data of Goan gauging station in Korea were performed based on Monte Carlo simulation. In order to consider uncertainties that can arise from model and data errors, kernel density estimation for fitting the sampling distributions was chosen to determine safety factors (SFs) that depend on the probability model used to fit the real data. The relative biases of Sheater and Jones plug-in (SJ) are the smallest in most cases among seven bandwidth selectors applied. The relative root mean square errors (RRMSEs) of the Gumbel (GUM) are smaller than those of any other models regardless of parent models considered. When the Weibull-2 is assumed as a parent model, the RRMSEs of kernel density estimation are relatively small, while those of kernel density estimation are much bigger than those of parametric methods for other parent models. However, the RRMSEs of kernel density estimation within interpolation range are much smaller than those for extrapolation range in comparison with those of parametric methods. Among the applied distributions, the GUM model has the smallest SFs for all parent models, and the general extreme value model has the largest values for all parent models considered.     

Synthetic regional flow duration curve for southern Taiwan

The primary purpose of this study is to develop the regional flow duration curves for southern Taiwan. To define homogeneous regions for developing regional flow duration curves, multivariate statistical analysis (principal component and cluster analysis) was applied to daily flow data from 34 stream-gauged stations in southern Taiwan. Two kinds of clustering variables, the dimensionless flow duration curve and specific flow duration curve, were compared in this study. It was found that three homogeneous regions delineated by specific flow duration curves as clustering variables have more reasonable results. The three homogeneous regions not only have well-defined geographical boundaries, but also correspond to the rainfall and geology characteristics of the regions. It seems that the technique of cluster analysis can reasonably define the homogeneous regions. In each homogeneous region, the synthetic regional flow duration curves were developed by a family of parametric duration curves. This approach has the advantage of being simple and needing only the basin area as an index. The performance of the regional flow duration curve was verified by the comparison of areas under the actual and synthetic flow duration curves; the latter were generated from the regional flow duration curve. Almost all the 34 stream-gauged stations had less than 25% absolute error.     

Intraseasonal predictability of the duration of flooding above National Weather Service flood warning levels across the U.S. Midwest

Unpreparedness is often the main cause of the economic and social damages caused by floods. To mitigate these impacts, short-term forecasting has been the focus of several studies during the past decades; however, less effort has been paid to flood predictions at longer lead times. Here, we use forecasts by six models from the North American Multi-Model Ensemble project with a lead time from 0.5 to 9.5 months to predict the seasonal duration of floods above four National Weather Service flood categories (“action,” “flood,” “moderate” and “major”). We focus on 202 U.S. Geological Survey gage stations across the U.S. Midwest and use a statistical framework which considers precipitation, temperature, and antecedent wetness conditions as predictors. We find that the prediction skill of the duration of floods for the “action” and “flood” categories is overall low, largely because of the low accuracy of the climate forecasts rather than of the errors introduced by the statistical models. The prediction skill slightly improves when considering the shortest lead times (i.e., from 0.5 to 2.5 months) during spring in the Northern Great Plains, where antecedent wetness conditions play an important role in influencing the generation of floods. It is very difficult to draw strong conclusions with respect to the “moderate” and “major” flood categories because of the limited number of available events.     

Non-identical models for seasonal flood frequency analysis

Abstract

The aim is to build a seasonal flood frequency analysis model and estimate seasonal design floods. The importance of seasonal flood frequency analysis and the advantages of considering seasonal design floods in the derivation of reservoir planning and operating rules are discussed, recognising that seasonal flood frequency models have been in use for over 30 years. A set of non-identical models with non-constant parameters is proposed and developed to describe flows that reflect seasonal flood variation. The peak-over-threshold (POT) sampling method was used, as it is considered to provide significantly more information on flood seasonality than annual maximum (AM) sampling and has better performance in flood seasonality estimation. The number of exceedences is assumed to follow the Poisson distribution (Po), while the peak exceedences are described by the exponential (Ex) and generalized Pareto (GP) distributions and a combination of both, resulting in three models, viz. Po-Ex, Po-GP and Po-Ex/GP. Their performances are analysed and compared. The Geheyan and the Baiyunshan reservoirs were chosen for the case study. The application and statistical experiment results show that each model has its merits and that the Po-Ex/GP model performs best. Use of the Po-Ex/GP model is recommended in seasonal flood frequency analysis for the purpose of deriving reservoir operation rules.     

地震动持时的研究进展

地震动持时作为表征地震动的三要素之一,其对震害的影响逐渐被人们所认识.然而,在地震动持时的定义方面,目前没有统一且明确的概念,文中给出了广义的地震动总持时和强震持时的定义,研究者们根据各自领域的研究特点选择更适合的持时.持时大致可以分为两个大类:一是绝对持时,即基于加速度绝对值阈值的括号持时;二是相对持时,也就是反映地震动过程强度或能量变化趋势的持时,比如能量控制的相对持时等.持时的定义有很多种,文章简单地回顾了地震动持时的五种定义,同时,细致地分析了五种持时定义所表现的特点,并介绍了持时预测模型的研究成果,最后针对目前应用持时存在的问题提出了几点认识.     

Significant duration predictive models developed from strong-motion data of thrust-faulting earthquakes recorded in Mexico City

Predictive models for estimating strong-motion duration in sites characterized by soft-soil profiles are presented in this paper. The models were developed using a strong-motion database that includes observations from subduction interface earthquakes that occurred from 1989 to 2020 and recorded in Mexico City, which is located at source-to-site distances up to 600 km. A linear mixed-effects regression model, which is a statistical fitting procedure that allows to consider the correlation structure of grouped data, was used to develop the predictive models. Relative significant duration was selected to measure strong-motion duration. This measure can be directly associated with the accumulation of energy of the ground movement. The proposed predictive models relate relative significant duration with moment magnitude, either hypocentral distance or closest distance to the rupture plane, and dominant period of the soil. Regression analyses were performed grouping the ground-motion data by both seismic event and site class. Model assumptions, such as homoscedasticity, normality, and linearity of effects, were verified from residual analyses. From the results, the expected value of the natural logarithm of relative significant duration was found to be ～1.2 times greater for an earthquake with a moment magnitude equal to 8.0 than for one of 6.0. An insightful discussion about the sources and character of the uncertainties detected in the proposed predictive models is also presented in this study. The predictive models proposed in this paper are of valuable application in seismic and structural engineering because they allow to circumscribe properly the dimension and randomness of strong-motion duration.     

非齐次复合 Poisson地震发生概率模型研究

依据现有地震发生概率模型合理性与局限性以及地震估计的基本思想提出五类非齐次复合 Poisson 地震发生概率模型,阐述各模型的基本特点及可能实用的前提。 以华北地区的地震序列为例大致模拟了不同阶段的地震发生概率水平,分析表明非齐次复合 Poisson 地震发生概率模型更能反映地震发生的时间不均匀性。     

Stochastic analysis of flood series

A stochastic model based on the renewal process was developed and used to analyse the characteristics of floods: the volume exceedence, the duration of the flood and the maximum annual flow. The model contains a method for determination of total annual volume exceedence and total annual duration of floods, as well as a method for calculation of maximum annual exceedence, maximum flood duration and maximum flow. The subset of the flood occurrence number in a given time interval is common for all analysed phenomena (volume exceedence, flood duration, maximum flow). The subset of given exceedences is common for total annual volume exceedence, as well as for maximum annual volume exceedence. The same holds for durations of individual floods. The model was then applied to analyse the floods on the Drina River at the Paunci hydrological station and on the Danube River at the Bezdan station.     

Effect of the duration and direction of storm movement on planar flow with full and partial areal coverage

Using kinematic wave equations, analytical solutions are derived for flow resulting from storms moving either up or down the plane and covering it fully or partially. By comparing the flow resulting from a moving storm with that from a stationary storm of the same duration and areal coverage, the influence of storm duration, direction and areal coverage is investigated. It is found that the direction, duration and areal coverage of storm movement have a pronounced effect on the discharge hydrograph. The runoff hydrographs resulting from storms moving downstream are quite different from those from storms moving upstream. Likewise, the areal coverage of the storm has a pronounced effect on the runoff hydrograph. Copyright © 2002 John Wiley & Sons, Ltd.     

Entropy-based inference of simple physical models for regional flood analysis

 Regional flood analysis is formulated as a physical-modelling problem consisting in the inference of meaningful physical models for a set of observable uncertain quantities representing floods, given the observed data separately associated with them. It is argued that physical modelling suitable for representing causality relationships should involve the use of models comprising functional dependences of the observable uncertain quantities with regard to other quantities which are unobservable. The regional physical-modelling problem becomes the selection, from any proposed space of candidate models, of a probability distribution for the unobservable uncertain quantities together with a functional-dependence model connecting the observable to the unobservable uncertain quantities. Due to the need to coherently represent observational data and to express precisely the available evidences, the physical modelling problem is formalized in a plausible logic language, within the logical probability framework. A logical inference procedure called the relative entropy method with fractile constraints (REF) is formulated within this framework and extended to solve the regional physical-modelling problem. Contrary to the current statistical methods, it allows the selection and validation of inferred models and can be applied whatever it is the number of observational data. The complete solution to the problem using the relative entropy procedure is presented. This method is applied to the regional modelling of annual maximum floods of a set of separate rivers in the Iberian Peninsula. For this application the space of candidate models includes several types of two-parameter probability distributions for the unobservable uncertain quantities and the class of linear homogeneous functional-dependence models connecting the observable to the unobservable quantities.     

Efficient strong motion duration of pulse-like records for nonlinear structural analyses

The special interest produced by near-field directivity records and their effect on structural response has given a new significance in the velocity time history, its pulse-like content, and relevant parameters and indices. Recent research has shown that directivity pulses inherent in these records govern the linear and the nonlinear response of a wide range of structures. Based on this observation, it is suggested in this paper that a truncated ground motion, limited to the duration of the predominant velocity pulse, can be efficiently used to predict the structural response, instead of the base motion with the total duration, reducing significantly the required runtimes. The proposed methodology is verified for a series of medium to high rise reinforced concrete buildings, for which nonlinear time-history analyses are performed for a vast suite of pulse-like near-field records applied as base excitations with their total duration and the proposed truncated one. Comparison of the results for the response displacements and forces shows very good agreement, permitting the acceptance of the pulse duration as the efficient strong motion time interval of the original record, which determines the response and, thus, it can be used for nonlinear structural analyses.