NON-ZERO LOWER LIMIT IN LOW FLOW FREQUENCY ANALYSIS?1

ABSTRACT: The implications of fitting distributions with non-zero lower limits to low flow data are examined. The 3-parameter Weibull distribution is fitted to annual minimum flow series from 60 long term stations in Canada. The relations between the estimated lower limit and three sampling variables (skewness, smallest, and largest observations) were investigated. The lower limit strongly depends on the sample skewness; it varies directly with the sample skewness, which in turn is highly influenced by the largest observation. For a given skewness, the value of the estimated lower limit is determined by the value of the smallest observation. Therefore, the lower limit cannot be accurately determined, and the resulting low flow estimates will be either too small or too high.     

A UNIFYING SET OF PROBABILITY TRANSFORMS FOR STOCHASTIC HYDROLOGY1

Abstract: An ordered set of probability sensity functions was derived form transforms of the normal distribution. Variate transforms are based on orders of exponentiation. The set of distributions includes the log-normal. a partial basis for use of these functins in hydrology is demonstrated by establishing some required properties. A concept of mixed samples of zero and nonzero elements forming nonseparable sets of virtual and real elements is introduced to establish a physical lower limit of sampled diata independent of functional bounds.     

STREAM TYPES IN THE DES MOINES RIVER BASIN1

Stream tributaries in the Des Moines River basin have been classified according to the glacial terrain through which they flow. Three stream types were categorized as follows: (1) streams that flow entirely on Wisconsin drift, (2) streams that flow entirely on Kansan drift, and (3) streams that have their headwaters located on new drift but have their lower reaches flowing on older drift. Selected channel and valley characteristics were measured and used to verify the stream type classification. Five variables were chosen for use in a multiple linear discriminatory analysis, which is a statistical technique developed for the purpose of classifying observations into one of several categories which have been predetermined. The streams in each group were verified with the exception of three anomalies based on the probability associated with the largest linear discriminant function. The rationale for the three anomalous streams is not easily determined. But, they are considered to be associated with pre-glacial drainage or at least pre-Wisconsin age drainage. Otherwise, the analysis shows that the major channels and valleys in the Des Moines River basin tend to reflect the glaciated upland surface.     

EVALUATION OF PROBABILITY DENSITY FUNCTIONS IN PRECIPITATION MODELS FOR THE PACIFIC NORTHWEST1

ABSTRACT: Recent work has found that a one-parameter Weibull model of wet day precipitation amount based on the Weibull distribution provides a better fit to historical daily precipitation data for eastern U.S. sites than other one-parameter models. The general two-parameter Weibull distribution was compared in this study to other widely used distributions for describing the distribution of daily precipitation event sizes at 99 sites from the U.S. Pacific Northwest. Surprisingly little performance was sacrificed by reducing the two-parameter Weibull to a single-parameter distribution. Advantages of the single-parameter model included requiring only the mean wet day precipitation amount for calibration, invertibility for simulation purposes, and ease of analytical manipulation. The fit of the single-parameter Weibull to the 99 stations included in this study was significantly better than other single-parameter models tested, and performed as well as the widely endorsed, more cumbersome, two-parameter gamma model. Both the one-and two-parameter Weibull distributions are shown to have b-moments that are consistent with historical precipitation data, while the ratio of b-skew and b-variance in the gamma model is inconsistent with the historical recerd by this measure. In addition, it was found that the two-parameter gamma distribution was better fit using the method of moments estimators than maximum likelihood estimates. These findings suggested that the distribution in precipitation among sites in the Pacific Northwest with dramatically different settings are nearly identical if expressed in proportion to the mean site event size.     

ESTIMATING PROBABLE MAXIMUM FLOOD PROBABILITIES1

ABSTRACT: Methods of computing probabilities of extreme events that affect the design of major engineering structures have been developed for most failure causes, but not for design floods such as the probable maximum flood (PMF). Probabilities for PMF estimates would be useful for economic studies and risk assessments. Reasons for the reluctance of some hydrologists to assign a probability to a PMF are discussed, and alternative methods of assigning a probability are reviewed. Currently, the extrapolation of a frequency curve appears to be the most practical alternative. Using 46 stations in the Mid-Atlantic region, the log-gamma, log-normal, and log-Gumbel distributions were used to estimate PMF probabilities. A 600,000-year return period appears to be a reasonable probability to use for PMFs in the Mid-Atlantic region. The coefficient of skew accounts for much of the variation in computed probabilities.     

ESTIMATING ANNUAL FLOOD PROBABILITIES USING FOURIER SERIES METHOD1

ABSTRACT: The Fourier series method is proposed as a feasible non-parametric approach for the estimation of the density and distribution functions of annual floods. Clearly, the goodness of fit to empirical data improves as higher Fourier terms are incorporated, and the choice of a higher term depends on whether the inclusion of this term will reduce the fitting error to within a specified tolerance level. This method was applied to the flood data from eight rivers, and to data simulated from known distributions. The results are clearly better than other parametric methods, just like other non-parametric techniques currently used to estimate annual flood probabilities.     

DERIVATION OF THE GAMMA DISTRIBUTION BY USING THE PRINCIPLE OF MAXIMUM ENTROPY (POME)1

The principle of maximum entropy (POME) was used to derive the two-parameter gamma distribution used frequently in synthesis of instantaneous or finite-period unit hydrographs. The POME yielded the minimally prejudiced gamma distribution by maximizing the entropy subject to two appropriate constraints which were the mean of real values and the mean of the logarithms of real values of the variable. It provided a unique method for parameter estimation. Experimental data were used to compare this method with the methods of moments, cumulants, maximum likelihood estimation, and least squares.     

For What Applications Can Probability and Non-Probability Sampling Be Used?

Almost any type of sample has some utilitywhen estimating population quantities. The focus inthis paper is to indicate what type or combination oftypes of sampling can be used in various situationsranging from a sample designed to establishcause-effect or legal challenge to one involving asimple subjective judgment. Several of these methodshave little or no utility in the scientific area buteven in the best of circumstances, particularlycomplex ones, both probabilistic and non-probabilisticprocedures have to be used because of lack ofknowledge and cost. We illustrate this with a marbledmurrelet example.     

华东地区地震目录的完全性分析

按照文献 [1]提出的分析方法 ,对华东地区地震发生率进行了统计修补 ,由此得到华东地区地震发生的概率密度分布。其结果对地震活动性研究和地震危险区的划分具有一定意义。在地震目录分段分析研究中 ,引入了Fisher的时序分割法     

应用极值理论研究台湾和华东地区中强地震活动的相关性

运用极值分布理论对1970～1999年间台湾和华东地区的地震资料进行统计性研究,得出其地震相应震级的复发周期[T(M)]、理论发震次数(η)和华东地区中强地震的发震概率阈值(PO)。通过对T(M)的同比分析,发现两地中强地震存在着较好的相关性。用以上研究的结果对华东地区5级以上地震的发震概率、发震时间和地震强度进行综合判定,效果较好。