Chowdhury and Stedinger's approximate confidence intervals for design floods for a single site

A basic problem in hydrology is computing confidence levels for the value of the T-year flood when it is obtained from a Log Pearson III distribution in terms of estimated mean, estimated standard deviation, and estimated skew. In an important paper Chowdhury and Stedinger [1991] suggest a possible formula for approximate confidence levels, involving two functions previously used by Stedinger [1983] and a third function, λ, for which asymptotic estimates are given. This formula is tested [Chowdhury and Stedinger, 1991] by means of simulations, but these simulations assume a distribution for the sample skew which is not, for a single site, the distribution which the sample skew is forced to have by the basic hypothesis which underlies all of the analysis, namely that the maximum discharges have a Log Pearson III distribution. Here we test these approximate formulas for the case of data from a single site by means of simulations in which the sample skew has the distribution which arises when sampling from a Log Pearson III distribution. The formulas are found to be accurate for zero skew but increasingly inaccurate for larger common values of skew. Work in progress indicates that a better choice of λ can improve the accuracy of the formula.     

Bootstrap confidence intervals for design storms from exceedance series

Abstract

An approach for better understanding of the physical implication of estimated aquifer parameters is demonstrated by analysing the pumping test data at Cottam in the Nottingham aquifer, UK. A sensitivity analysis showed that the area represented by the estimated parameters was much smaller than the area covered by the depression cone. After parameters are estimated, further research should be carried out to understand what portions of the aquifer the parameters represent. The parameters estimated at Cottam represented mainly aquifer features between roughly 100 and 2000 m. The sensitivity analysis also showed that the observed drawdown being satisfactorily matched by a model with uniform parameters does not prove that the aquifer is homogeneous. Slightly anomalous data may imply the existence of large anomalous zones. Although the drawdowns at Cottam could be ‘satisfactorily’ fitted by a model with uniform parameters, the fit could be improved by a model using a more permeable aquifer but with a zone about 700 m wide and with 42% less transmissivity.     

Evaluation of confidence intervals for a steady-state leaky aquifer model

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. & Cooley, R.L., Water Resources Research, 1987, 23(7), 1237–1250] was used to calculate nonlinear Scheffé-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km² of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.     

Estimation of quantiles and confidence intervals for the log-Gumbel distribution

The log-Gumbel distribution is one of the extreme value distributions which has been widely used in flood frequency analysis. This distribution has been examined in this paper regarding quantile estimation and confidence intervals of quantiles. Specific estimation algorithms based on the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood (ML) are presented. The applicability of the estimation procedures and comparison among the methods have been illustrated based on an application example considering the flood data of the St. Mary's River.     

Estimation of confidence intervals of quantiles for the Weibull distribution

 Estimation of confidence limits and intervals for the two- and three-parameter Weibull distributions are presented based on the methods of moment (MOM), probability weighted moments (PWM), and maximum likelihood (ML). The asymptotic variances of the MOM, PWM, and ML quantile estimators are derived as a function of the sample size, return period, and parameters. Such variances can be used for estimating the confidence limits and confidence intervals of the population quantiles. Except for the two-parameter Weibull model, the formulas obtained do not have simple forms but can be evaluated numerically. Simulation experiments were performed to verify the applicability of the derived confidence intervals of quantiles. The results show that overall, the ML method for estimating the confidence limits performs better than the other two methods in terms of bias and mean square error. This is specially so for γ≥0.5 even for small sample sizes (e.g. N=10). However, the drawback of the ML method for determining the confidence limits is that it requires that the shape parameter be bigger than 2. The Weibull model based on the MOM, ML, and PWM estimation methods was applied to fit the distribution of annual 7-day low flows and 6-h maximum annual rainfall data. The results showed that the differences in the estimated quantiles based on the three methods are not large, generally are less than 10%. However, the differences between the confidence limits and confidence intervals obtained by the three estimation methods may be more significant. For instance, for the 7-day low flows the ratio between the estimated confidence interval to the estimated quantile based on ML is about 17% for T≥2 while it is about 30% for estimation based on MOM and PWM methods. In addition, the analysis of the rainfall data using the three-parameter Weibull showed that while ML parameters can be estimated, the corresponding confidence limits and intervals could not be found because the shape parameter was smaller than 2.     

Comparison of bootstrap confidence intervals for an ANN model of a karstic aquifer response

Following many applications artificial neural networks (ANNs) have found in hydrology, a question has been rising for quantification of the output uncertainty. A pre‐optimized ANN simulated the hydraulic head change at two observation wells, having as input hydrological and meteorological parameters. In order to calculate confidence intervals (CI) for the ANN output two bootstrap methods were examined namely bootstrap percentile and BCa (Bias‐Corrected and accelerated). The actual coverage of the CI was compared to the theoretical coverage for different certainty levels as a means of examining the method's reliability. The results of this work support the idea that the bootstrap methods provide a simple tool for confidence interval computation of ANNs. Comparing the two methods, the percentile requires fewer calculations and yields narrower intervals with similar actual coverage to that of BCa. Overall, the actual coverage was proved lower than desired when not modeled points were present in the data subset. Copyright © 2011 John Wiley & Sons, Ltd.     

Bivariate drought frequency curves and confidence intervals: a case study using monthly rainfall generation

Although water resources management practices recently use bivariate distribution functions to assess drought severity and its frequency, the lack of systematic measurements is the major hindrance in achieving quantitative results. This study aims to suggest a statistical scheme for the bivariate drought frequency analysis to provide comprehensive and consistent drought severities using observed rainfalls and their uncertainty using synthesized rainfalls. First, this study developed a multi-variate regression model to generate synthetic monthly rainfalls using climate variables as causative variables. The causative variables were generated to preserve their correlations using copula functions. This study then focused on constructing bivariate drought frequency curves using bivariate kernel functions and estimating their confidence intervals from 1,000 likely replica sets of drought frequency curves. The confidence intervals achieved in this study may be useful for making a comprehensive drought management plan through providing feasible ranges of drought severity.     

Quantifying differences between reservoir inflows and dam site floods using frequency and risk analysis methods

Reservoirs are the most important constructions for water resources management and flood control. Great concern has been paid to the effects of reservoir on downstream area and the differences between inflows and dam site floods due to the changes of upstream flow generation and concentration conditions after reservoir’s impoundment. These differences result in inconsistency between inflow quantiles and the reservoir design criteria derived by dam site flood series, which can be a potential risk and must be quantificationally evaluated. In this study, flood frequency analysis (FFA) and flood control risk analysis (FCRA) methods are used with the long reservoir inflow series derived from a multiple inputs and single output model and a copula-based inflow estimation model. The results of FFA and FCRA are compared and the influences on reservoir flood management are also discussed. The Three Gorges Reservoir (TGR) in China is selected as a case study. Results show that the differences between the TGR inflow and dam site floods are significant which result in changes on its flood control risk rates. The mean values of TGR’s annual maximum inflow peak discharge and 3 days flood volume have increased 5.58 and 3.85% than the dam site ones, while declined by 1.82 and 1.72% for the annual maximum 7 and 15 days flood volumes. The flood control risk rates of middle and small flood events are increased while extreme flood events are declined. It is shown that the TGR can satisfy the flood control task under current hydrologic regime and the results can offer references for better management of the TGR.     

Estimation of confidence interval for hydrological design value for some continuous distributions under complete and censored samples

The quantile of a probability distribution, known as return period or hydrological design value of a hydrological variable is the value corresponding to fixed non-exceedence probability and is very important notion in hydrology. In hydraulic engineering design and water resources management, confidence interval (CI) estimation for a population quantile is of primary interest and among other applications, is used to assess the pollution level of a contaminant in water, air etc. The accuracy on such estimation directly influences the engineering investments and safety. The two parameter Weibull, Pareto, Lognormal, Inverse Gaussian, Gamma are some commonly used probability models in such applications. In spite of its practical importance, the problem of CI estimation of a quantile of these widely applicable distributions has been less attended in the literature. In this paper, a new method is proposed to obtain a CI for a quantile of any distribution for which [or the probability distribution of any one-to-one function of the underlying random variable (RV)] generalized pivotal quantities (GPQs) exist for its parameters. The proposed method is elucidated by constructing CIs for quantiles of Weibull, Pareto, Lognormal, Extreme value distribution of type-I for minimum, Exponential and Normal distributions for complete as well as type II singly right censored samples. The empirical performance evaluation of the proposed method evinced that the proposed method has exact well concentrated coverage probabilities near the nominal level even for small uncensored samples as small as 5 and for censored samples as long as the proportion of censored observations is up to 0.70. The existing methods for Weibull distribution have poor or dispersed coverage probabilities with respect to the nominal level for complete samples. Applications of the proposed method in ground water monitoring and in the assessment of air pollution are illustrated for practitioners.     

单台测震分析辅助软件的设计及实现

介绍了一种适合于单台测震分析的辅助软件。该软件对我国需要的测震五日报及月报报告,具有全面的处理能力;对EDSP-IAS测震分析软件形成的震相文件,通过自动计算可以生成地震报告,无须人工干预;对台站经常使用的震相走时便查表可以方便的采用任意两个参数进行查询;对台站涉及的震级计算、震中距计算等功能提供良好的运用界面。从腾冲台的实际运用效果来看,该软件可以为台站测震分析提供一个比较理想的辅助工具。     

Newmark design spectra considering earthquake magnitudes and site categories

Newmark design spectra have been implemented in many building codes, especially in building codes for critical structures. Previous studies show that Newmark design spectra exhibit lower amplitudes at high frequencies and larger amplitudes at low frequencies in comparison with spectra developed by statistical methods. To resolve this problem, this study considers three suites of ground motions recorded at three types of sites. Using these ground motions, influences of the shear-wave velocity, earthquake magnitudes, source-to-site distances on the ratios of ground motion parameters are studied, and spectrum amplification factors are statistically calculated. Spectral bounds for combinations of three site categories and two cases of earthquake magnitudes are estimated. Site design spectrum coefficients for the three site categories considering earthquake magnitudes are established. The problems of Newmark design spectra could be resolved by using the site design spectrum coefficients to modify the spectral values of Newmark design spectra in the acceleration sensitive, velocity sensitive, and displacement sensitive regions.     

设计地震动参数确定中的场地影响考虑

讨论了场地条件对场地设计地震动参数的影响问题,对国际上一些国家的抗震设计规范考虑该问题的相关规定作了介绍和分析,探讨了抗震设计对该问题处理的发展趋势,基于相关的强震纪录统计分析和场地模型计算反应分析已有的结果,研究了场地条件对场地设计地震动参数的影响特点和规律,重点考虑了场地类别和场地土体非线性的影响。结果这些分析与探讨结果,建议了用于不同类别场地设计地震动参数确定的一组经验系统。     

Statistical damage detection method for frame structures using a confidence interval

<正>A novel damage detection method is applied to a 3-story frame structure,to obtain statistical quantification control criterion of the existence,location and identification of damage.The mean,standard deviation,and exponentially weighted moving average(EWMA) are applied to detect damage information according to statistical process control(SPC) theory.It is concluded that the detection is insignificant with the mean and EWMA because the structural response is not independent and is not a normal distribution.On the other hand,the damage information is detected well with the standard deviation because the influence of the data distribution is not pronounced with this parameter.A suitable moderate confidence level is explored for more significant damage location and quantification detection,and the impact of noise is investigated to illustrate the robustness of the method.     

地震现场应急指挥技术系统的结构与设计

地震现场应急指挥工作是防震减灾的重要组成部分, 地震现场各种信息获取与传输是其重要内容, 有关灾情的资料是政府部门防震减灾决策的重要依据。 “十五”期间, 将建设地震现场应急指挥技术系统, 目前我国在这方面的研究和建设尚处于初级阶段, 其体系结构、 关键构成、 设计和实现还有许多值得进一步研究和探讨。 文中根据“九五”的建设过程, 对该技术系统的体系结构进行了论述, 提出了初步设计方案和技术框架, 并就今后发展进行了讨论。     

Numerical and approximate solutions for lithospheric thickening and thinning

Lithospheric thickness, surface heat flow and subsidence are calculated numerically as functions of time since the formation of oceanic lithosphere at a ridge crest. These numerical results confirm the validity of a previously derived approximate solution to the same problem. A numerical solution is also calculated for lithospheric thinning due to a sudden increase of heat flux into the base of the lithosphere. With this solution as a standard, an approximate solution is derived which can accurately predict thickness, heat flow, and uplift as functions of time. Lithospheric thinning and surface uplift begin immediately with the increase of heat flux at depth, but the increase in surface heat flow begins 20–40 m.y. later.     

砂土液化对设计反应谱和场地分类的影响

本文采用有效应力原理分析了液化土层对设计反应谱的影响，分析中考虑了砂层的厚度、埋深和输入地震动等因素。选择Ⅱ类场地，将其标准反应谱合成的三条地震加速度时程在考虑土层非液化下反演到基岩，再正演计算存在液化层时的地面运动时程和反应谱。分析结果表明，从特征周期的变化来看，液化土层使Ⅱ类场地易变为Ⅳ类场地，对地震影响系数的作用则不是很大，但频谱上0．8s是一个分界线，液化土层对分界线以下的高频分量有一定减震效果，对分界线以上的低频分量有显著的放大效应。     

Global projections of changing risks of floods and droughts in a changing climate

Abstract

Simulated daily discharge derived from a relatively high-resolution (approximately 1.1-degree) general circulation model was used to investigate future projections of extremes in river discharge under global warming. The frequency of floods was projected to increase over many regions, except those including North America and central to western Eurasia. The drought frequency was projected to increase globally, while regions such as northern high latitudes, eastern Australia, and eastern Eurasia showed a decrease or no significant changes. Changes in flood and drought are not explained simply by changes in annual precipitation, heavy precipitation, or differences between precipitation and evapotranspiration. Several regions were projected to have increases in both flood frequency and drought frequency. Such regions show a decrease in the number of precipitation days, but an increase in days with heavy rain. Several regions show shifts in the flood season from springtime snowmelt to the summer period of heavy precipitation.     

Estimation of discharges of water flows and debris floods in a small watershed

Floods in small mountainous watersheds cover a wide spectrum of flow. They can range from clear water flows and hyperconcentrated flows to debris floods and debris flows, and calculation of the peak discharge is crucial for predicting and mitigating such hazards. To determine the optimal approach for discharge estimation, this study compared water flow monitoring hydrographs to investigate the performance of five hydrological models that incorporate different runoff yields and influx calculation methods. Two of the models performed well in simulating the peak discharge, peak time, and total flow volume of the water flood. The ratio (γ) of the monitored debris flood discharge (Q_d) to the simulated water flow discharge (Q_w) was investigated. Qualitatively, γ initially increased with Q_w but then decreased when Q_w exceeded a certain threshold, which corresponded to rainfall of 95 and 120 mm in a 6- and 24-h event with a normal distribution of precipitation, respectively. The decrease might be attributable to a threshold of sediment availability being reached, beyond which increased flow rate is not matched by increased sediment input in the large watershed. Uncertainty of hydrological calculation was evaluated by dividing the catchment into sub-basins and adopting different rainfall time steps as input. The efficiency of using a distributed simulation exhibited marginal improvement potential compared with a lumped simulation. Conversely, the rainfall time step input significantly affected the simulation results by delaying the peak time and decreasing the peak discharge. This research demonstrates the applicability of a discharge estimation method that combines a hydrological water flow simulation and an estimation of γ. The results were verified on the basis of monitored flow densities and videos obtained in two watersheds with areas of 2.34 and 32.4 km².